Eduardo grew up in the Rio de Janeiro neighbourhood of Bangu and made his first steps in club football with CBF Nova Kennedy and Bangu Atlético Clube, although he did not play regularly in the youth categories. He was later noticed by Dinamo Zagreb’s scouts and joined the club’s youth squad in September 1999. Eduardo stayed at Dinamo on trial until December 1999 and returned to the club in February 2000, starting to play regularly for their under-17 squad. Eduardo found his way to the first team in the summer of 2001, despite suffering some injuries early in his career.

In 2002, Eduardo took Croatian citizenship and was first called up to play for the country’s Under-21 team at the finals tournament of the 2004 European Under-21 Championship in Germany. He appeared in all three of Croatia’s matches before they were eliminated from the tournament in the group stage. Eduardo also scored one goal in his international debut against Serbia and Montenegro national under-21 side. Eduardo was also called up to the Croatia team for the 2006 European Under-21 Championship qualifiers, in which he made a total of nine appearances and scored seven goals. However, Croatia failed to qualify for the final tournament after losing 5–2 on aggregate to Serbia and Montenegro in the play-offs, where Eduardo scored both of Croatia’s goals. He won a total of twelve international caps and scored eight goals.

Coming back from loan at Inter Zaprešić for the 2003–04 season, Eduardo quickly established himself as a regular in Dinamo Zagreb’s first team. He was subsequently named the best player of the Croatian league in 2004 as well as in 2006 and 2007, when he was one of the key players in Dinamo Zagreb’s team that won two consecutive titles in the Croatian league as well as one title in the Croatian Cup. In 2006, he also helped Dinamo winning the Croatian Supercup, scoring two goals in their 4–1 victory over Rijeka.

In the meantime, he was also called up a couple of times to play for the Croatia national football team. He made his international debut at senior level as a second-half substitute in the team’s friendly match against the Republic of Ireland on 16 November 2004 at the age of 21. In 2005, he appeared in another two friendly matches for the Croatian team and also played in both of the team’s two matches at the 2006 Carlsberg Cup in Hong Kong. He scored his first international goal for Croatia at the tournament, netting the third goal in the team’s 4–0 victory over hosts Hong Kong in the third-place play-off on 1 February 2006. He was subsequently also a candidate for joining the national team at the 2006 World Cup finals in Germany, but in the end did not get called up by the team’s then-coach, Zlatko Kranjčar, who commented that Eduardo “is a young player”, that he “does not diminish his value” by not selecting him, and that he “most seriously counts on him in future matches”.

In the 2006–07 season, he scored five goals in six matches for Dinamo Zagreb in two qualifying rounds for the Champions League and in the first round of the UEFA Cup. After netting a brace in Dinamo Zagreb’s 4–1 away win at Ekranas, he went on to score the first European goal at Arsenal’s new Emirates Stadium in London on 23 August 2006 as Dinamo Zagreb suffered a 5–1 aggregate defeat in the third qualifying round for the Champions League. He also scored both goals in Dinamo’s 5–2 aggregate defeat to Auxerre in the first round of the UEFA Cup on 14 September 2006.

Eduardo performed best for Dinamo Zagreb in the Croatian championship, netting 18 goals in 18 matches until the winter break of the 2006–07 season, including three braces and a hat-trick, and adding another seven assists to his tally. In addition to this, he was the only player who appeared in all of the club’s 18 matches before the winter break, also being in the starting lineup in each of the 18 matches. In mid-November 2006, he scored two hat-tricks in two consecutive matches he played for Croatia and Dinamo Zagreb in a period of four days.

After the 2006 World Cup, Eduardo returned to the national team under new coach Slaven Bilić and started Croatia’s friendly match against Italy on 16 August 2006, scoring the first goal in Croatia’s 2–0 victory. He would later establish himself as one of the key players in Croatia’s qualifying campaign for the Euro 2008. He made his competitive debut at senior international level in Croatia’s goalless away draw against Russia on 6 September 2006 and went on to score his first competitive international goal for Croatia on 11 October 2006 in their 2–0 home win against England, when he opened the scoring by sending a looping header over the stranded Paul Robinson. In the following qualifier, away to Israel on 15 November 2006, Eduardo netted a hat-trick to help Croatia to drive home a narrow 4–3 victory over the strong Israeli side.

In Dinamo’s 4–0 derby win over Zagreb on 12 May 2007, Eduardo scored his 30th and 31st league goals of the 2006–07 season and became the most successful Croatian league goalscorer of all time, breaking a 13-year-old record set by former Dinamo Zagreb striker Goran Vlaović with 29 goals scored for the club in the 1993–94 season. He finished the league season with 34 goals in 32 appearances. In the final league match of the season on 19 May 2007, he became the first player ever to score a hat-trick in the Eternal derby between Dinamo Zagreb and Hajduk Split, netting all three goals as Dinamo won the match 3–0.

On 3 July 2007, Arsenal confirmed that terms had been agreed with Dinamo Zagreb for the transfer of Eduardo for an undisclosed fee, believed to be around £7.5 million, subject to receiving a work permit. The initial work permit application was turned down by the Home Office, but the appeal hearing on 2 August reversed the decision.

Eduardo made his Premier League debut on 19 August 2007 in Arsenal’s 1–1 draw at Blackburn Rovers. Ten days later, he netted his first competitive goal for the Gunners in their Champions League qualifier against Sparta Prague, which Arsenal won 3–0. Eduardo scored his first group-stage goal in the Champions League on 19 September 2007 against Sevilla. While still fighting to find his place as a regular in the Premier League for Arsenal, Eduardo continued to display his goalscoring abilities in the League Cup, scoring two braces in two consecutive matches for the club, against Sheffield United and Blackburn Rovers, and helping them to reach the semi-finals of the competition. Eduardo found more playing time in all competitions due to Robin van Persie’s lengthy injury and found himself partnering Emmanuel Adebayor more often.

Eduardo finally managed to establish his place in Arsenal’s starting line-up in the Premier League over Christmas and New Year period, scoring his first two Premier League goals in a 4–1 win at Everton on 29 December 2007, first leveling the score and then putting Arsenal 2–1 up in the opening 15 minutes of the second half. On New Year’s Day 2008, he opened the scoring after only 72 seconds of the match against West Ham United; Arsenal went on to win 2–0. On the first weekend of the new year, he had a successful FA Cup debut as Arsenal faced Championship side Burnley on the road, first scoring the opening goal early on, and then setting up a second for Nicklas Bendtner midway through the second half. In the following three matches in January, he set up three more goals, providing two assists and winning a penalty. He went on to help Arsenal to return to the top of the Premier League in early February, scoring a skillful over-the-shoulder flick in a 3–1 away victory over Manchester City and assisting Philippe Senderos for an early goal in a 2–0 win over Blackburn Rovers at the Emirates.

In Croatia’s next qualifier, their first competitive game of the year 2007, at home against the sturdy Macedonian outfit on 24 March 2007, Eduardo scored the winner in the 88th minute to hand Croatia a 2–1 victory after trailing 1–0 at halftime. He went on to be Croatia’s saviour in both of their qualifiers against Estonia, scoring all three goals in Croatia’s 1–0 away and 2–0 home victories, as well as in their final home qualifier against Israel on 13 October 2007, where he netted the only goal in Croatia’s 1–0 victory. He also set up Ivica Olić to score Croatia’s 2nd goal in their famous 3–2 victory over England at Wembley—a win which saw England fail to qualify for Euro 2008. He finished the qualifying campaign with 10 goals in 12 matches and was the second-best goalscorer of the competition, after Northern Ireland’s David Healy with 13 goals.

On 23 February 2008, Eduardo suffered a broken left fibula and an open dislocation of his left ankle in a match against Birmingham City, following a tackle by Martin Taylor, for which Taylor was sent off. Eduardo was immediately taken to Selly Oak Hospital, where he underwent surgery. Gilberto Silva was the only person in the vicinity who spoke both Portuguese and English and was able to translate communication between Eduardo and the medical team. Eduardo’s injury was so graphic that Sky Sports, which was broadcasting the game live, decided not to show replays of the incident. Arsène Wenger initially called for a lifetime ban for Taylor, but retracted his comments later. Taylor claimed to have visited Eduardo in hospital and that an apology was accepted; Eduardo, however, could not remember Taylor’s visit or even the tackle. Some cite the incident as a cause of Arsenal failing to maintain their lead in the Premier League title race that season.

On 16 February 2009, Eduardo started against Cardiff City in the FA Cup, scoring in the 21st minute and converted a penalty in the second half. However, in that game, he suffered a hamstring injury. He returned against Burnley in the 5th round of the FA Cup, captaining the side and scoring Arsenal’s second goal. He made his first appearance in the Premier League after the injury on the opening day of the 2009–10 season against Everton. He scored Arsenal’s sixth goal in a 6–1 victory.

A week later, Eduardo was accused of simulation by the Scottish FA chief executive Gordon Smith to win a penalty in the 3–1 Champions League win over Celtic; Smith also demanded a ban for the striker. On 28 August, Eduardo was charged by UEFA with “deceiving the referee” over the penalty incident and subsequently punished with a two-match European ban, However, the ruling was overturned on appeal with Arsenal producing video evidence showing the claim of simulation was inconclusive and testimony supporting the appeal also coming from Manuel Enrique Mejuto González, who had awarded the penalty. Eduardo later scored the winning goal in Arsenal’s 3–2 win over Standard Liège on 16 September 2009. In November 2009, Eduardo signed a new long-term contract with Arsenal. He then scored his second Premier League goal of the season against Hull City on 19 December and scored again eleven days later in the 4–1 win over Portsmouth. Eduardo headed the winner in a 2–1 win over West Ham United to put Arsenal in the fourth round of the FA Cup on 3 January 2010. However, Arsenal were subsequently knocked out by Stoke City 3–1 at the Britannia Stadium.

After recovering from the leg injury, Eduardo made his first international appearance in just over a year, coming on as a substitute to replace Ivica Olić in the final 30 minutes of the friendly match against Romania on 11 February 2009, which saw Croatia recording a 2–1 away win. In the course of the same year, he made four appearances and scored three goals in Croatia’s unsuccessful qualifying campaign for the 2010 FIFA World Cup.

On 21 July 2010, he signed for Shakhtar Donetsk on a four-year contract for an undisclosed fee, believed to be in the region of £6 million. He made his Ukrainian Premier League debut on 7 August 2010, playing the first half and netting the second goal in a 5–0 win against PFC Sevastopol. Shakhtar and Arsenal were both drawn into Group H in the Champions League, something Eduardo hoped would not happen prior to the draw. Eduardo scored his second goal in an away game against FC Volyn Lutsk, coming on as a substitute, to give Shakhtar a 0–1 win. His third goal came in the Ukrainian Cup against FC Kryvbas Kryvyi Rih where, after coming on as a substitute, he scored the fifth goal in a 6–0 win. He then scored in the next match against FC Metalist Kharkiv, again coming on as a substitute, to level the game at 1–1, which Shakhtar went on to win 1–2 in a dramatic late fashion.

Returning to the Emirates Stadium on 19 October 2010 for Shakhtar’s UEFA Champions League group match with Arsenal, Eduardo came on as a substitute with his new side 3–0 down and received a standing ovation from the Arsenal supporters. He scored a late consolation goal for Shakhtar in a game that Arsenal went on to win 5–1, at which point the Arsenal fans rose again and cheered their former hero. In the rematch, he scored the winning goal in a 2–1 victory and refused to celebrate, showing respect for his former club.

On 5 April 2014, Eduardo scored 2 out of the 3 goals for Shakhtar Donetsk against Karpaty Lviv in a League game. The first goal came when teammate and compatriot, Darijo Srna, crossed the ball in from a corner, Eduardo headed the ball into the centre of the goal. The second goal came when Srna chipped the ball over a player to Luiz Adriano who chested the ball and fired the ball into the box for Eduardo to slot the ball into the goal once again. Shakhtar Donetsk were 2–0 up at half time and later finished the game 3–0 when Luiz Adriano out muscled two players to slot the ball into the bottom left corner.

It was announced on 17 July 2014 that he had signed for Brazilian side Flamengo. The forward scored his first goal for the club on 10 August 2014, in a match against Sport.

After making seven appearances and scoring two goals in the qualifying campaign, Eduardo was selected to be part of Croatia’s squad for the 2014 FIFA World Cup finals in his native Brazil. He did not feature in the defeat to the hosts in the opening match of the tournament, but came on for the last 21 minutes of the 4–0 win over Cameroon in the second group game, in place of Ivica Olić, to make his only appearance at the tournament, which saw Croatia eliminated in the group stage once again. On 15 July 2014, following the World Cup, Eduardo announced his retirement from the national team.

On 10 July 2015, Eduardo signed a one and a half-year contract with his old club Shakhtar Donetsk.

In February 2017, Eduardo returned to Brazil to sign for Atlético Paranaense in Série A.