Sadiku was born on 27 May 1991 in the municipality of Elbasan Country, Cërrik. His father, Durim, is from Trebisht, Albania and his mother from Podujevo, Kosovo. Sadiku is related to Taulant and Granit Xhaka through his mother. He is of paternal Bulgarian ancestry. His brother, Sherif Sadiku, is also a professional footballer who plays for Shkumbini Peqin in the Albanian First Division. Sadiku has cited his role model and favourite footballer the Swedish striker Zlatan Ibrahimović, and is also fan of Italian club Internazionale.

In July 2009, Sadiku completed a transfer to newly promoted Albanian Superliga side Gramozi Ersekë, owned by the brother of Albanian oil tycoon Rezart Taci. He made his first top flight appearance on 23 August at the age of 18 in the opening matchday against Shkumbini Peqin which ended in a goalless draw, with Sadiku coming on in the second half.

During the summer transfer window, Sadiku signed for his hometown club Elbasani. During the 2010–11 season first-half he played 14 matches and scored 5 goals. He made his debut with the club on 22 August 2010 during the opening league match against Tirana at home, playing 75 minutes in a 1–1 draw. He scored his first goal of the season in his second appearance six days later, netting a last-minute winner in a 2–1 away win over Bylis Ballsh.

On 19 December 2010, during the league match against Laçi, Sadiku, who had scored earlier in the match, was sent-off in the 82nd minute. A minute before his dismissal, he scored but was caught offside by the assistant referee Eduard Miho, which enraged Sadiku, who run towards him and pushed away by throat, spitting and also insulted him the process. Disciplinary Committee suspended Sadiku from Albanian football for two years, also fining him. That was his last match in Albanian football, as Sadiku left the club to purchase a career in Switzerland. As it happened with Gramozi Ersekë in previous season, Elbasani also ranked in the last place and were relegated to Albanian First Division.

Sadiku moved for the first time aboard in March 2011 where he completed a transfer to Swiss Challenge League side Locarno. The transfer was made official on 13th. He arrived in the morning and even travelled with the side to the away fixture with Schaffhausen. He made his debut later that day, playing for 82 minutes in a 2–1 loss. He opened his scoring account on Switzerland on his third appearance for the club, netting the winning goal against Chiasso on 1 April for a 2–1 win.

On 23 July 2012, Locarno confirmed via their official website the purchase of Sadiku on a three-year contract. With the deal Sadiku would earn CHF200,000 per season.

New Albania senior team coach Gianni De Biasi, called up Sadiku for his first match as a head coach, a friendly against Georgia on 29 February 2012 at Mikheil Meskhi Stadium in Tbilisi. He made his senior international debut in the game, coming on as an 82nd-minute substitute for goalscorer and fellow debutant Edgar Çani in the 2–1 loss for Albania. He was called up then to Albania’s next two friendliest against Qatar and Iran in May 2012, where he played as a second-half substitute in both games, which Albania won them both.

On 13 November 2013, Zürich and Lugano reached an agreement for the transfer of Sadiku for €500,000. The transfer was made official on 1 January 2014 where the player signed a contract until June 2018, taking squad number 11. At Zürich, he found his Albania teammate Burim Kukeli.

In the 2013 UEFA European Under-21 Championship qualification Sadiku scored two goals as a second-half substitute against Moldova U21 on 7 September 2011 to earn Albania their first points of the campaign. He then scored twice against Poland in a 3–4 loss for Albania. He followed this up with another two goals in a 2–2 draw with Portugal, taking his tally to 6 goals in his first 7 games for Albania U21.

He is also known to be a supporter of Socialist Party of Albania, having taken part in 2013 and 2017 electoral campaign. On 30 December 2016, Sadiku was named “Honorary Citizen” of Elbasan for his contributions to sports. On 9 January 2018, Sadiku was engaged to Elona, a Kosovo Albanian dentist, which was one of his fans that he met via Facebook.

On 10 May 2014, during the league match against St. Gallen, Sadiku entered as substitute in the 70th minute and was injured shortly after, breaking knee ligament which would keep him sidelined for the next 6 months.

Sadiku made his on-field return on 30 November 2014 in 2014–15 Swiss Super League matchday 17 versus Basel where he came as a substitute in a 1–2 home loss. He opened his scoring account for 2014–15 season during the 5–0 win over Cham for Swiss Cup Round 3. He concluded 2014–15 season by scoring 3 goals in 14 league appearances, in addition 1 goal in 1 cup match.

For the 2014 FIFA World Cup qualifiers, new coach Gianni De Biasi had introduced young forwards into the senior national team to create more competition for places in the team. Young forwards such as Sadiku was among Edgar Çani and Bekim Balaj provided competition for the established and mature internationals which were Erjon Bogdani and Hamdi Salihi. In the opening match against Cyprus for the 2014 FIFA World Cup qualifiers on 7 September 2012, Sadiku managed to play as a starter among Salihi forming the duo strikers partnership and Sadiku himself managed to score his first international goal. His goal came in the 36th minute after a cross from free-kick in the right side by Alban Meha and it was the opening goal of the game to open Albania’s way towards a 3–1 win.

Sadiku was not called regularly during the UEFA Euro 2016 qualifying campaign; even when he was part of the squad, he was seen as the third choice by manager De Biasi, ranked behind Cikalleshi and Balaj. He made his first appearance in Group I on 4 September 2015 versus Denmark, replacing Lenjani at 64th minute as Albania took a goalless draw at Telia Parken. In the final matchday against Armenia on 11 October, Sadiku came on at 59th minute and netted 17 minutes later to make the score 3–0; his weak shot inside the box was enough to beat goalkeeper Kasparov after a cross by Roshi. This win cemented Albania the second place in Group I which secured them a place at UEFA Euro 2016, in its first ever appearance at major football tournament.

During the first part of 2015–16 season, Sadiku was used scarcely, and often as a substitute by coach Sami Hyypiä despite being the team’s top goalscorer in the league. That lead him to request a loan to another Swiss Super League side in order to play more to be ready to represent Albania in the UEFA Euro 2016 in France. His wish was fulfilled and on 12 January 2016 Sadiku was loaned out to the bottom-side Vaduz until the end of season. During his presentation one day later, Sadiku was allocated squad number 32 and dubbed his Vaduz move as the “right decision”. His parent club Zürich was criticized by the Swiss media, which dubbed the loan an “own goal” and an “arrogant” decision.

On 21 May 2016, Sadiku was named in Albania’s preliminary 27-man squad for UEFA Euro 2016, and in Albania’s final 23-man UEFA Euro 2016 squad on 31 May. He made his first ever UEFA European Championship appearance on 11 June 2016 in the opening Group A match against Switzerland as Albania conceded early and lost 0–1. In the final group match versus Romania eight days later, Sadiku netted a header in the first half to lead the team to a historic 1–0 win; in doing so, he became the first Albanian player to score a goal in the UEFA European Championship and Albania took their first ever win in a major football tournament. It was also Albania’s first win over Romania since 1948. Albania finished the group in the third position with three points and with a goal difference –2, and was ranked last in the third-placed teams, which eventually eliminated them.

For the qualifiers of 2018 FIFA World Cup qualification, Sadiku’s Albania was placed in Group G along with Spain, Italy, Israel, Macedonia and Liechtenstein. On 29 August 2016, he was in the team’s for the friendly against Morocco and the opening qualifying match against Macedonia. He played as a second-half substitute in team’s goalless draw against Morocco at the newly renovated Loro Boriçi Stadium. On 5 September in the match against Macedonia, Sadiku opened the score with right-footed shoot just outside the box as Albania won 2–1 thanks to a goal in the last minutes. Later that month, Sadiku suffered an injury while playing for Zürich which kept him sidelined for the next two qualifying match against Liechtenstein and Spain in October, which ended respectively with a 2–0 win and 0–2 defeat. He also missed the match at Elbasan Arena against Israel which ended in a 0–3 defeat as Albania was dropped to fourth place.

In April 2016, Sadiku signed a sponsorship deal with American sportswear and equipment supplier, Nike.

On 12 July 2017, Sadiku joined Polish Ekstraklasa side Legia Warsaw by penning a three-year contract. The transfer fee was undisclosed, but it was reported that Legia paid €1.5 million for his services, making Sadiku the most expensive purchase of Polish football. He was presented two days later, where he was given squad number 99, stating: “I am happy I have signed with such a great club. This is a good step in my career. I hope we will qualify for the Champions League group stage.”

Sadiku returned to the national team in March for the match against Italy and the friendly against Bosnia and Herzegovina. He returned to the field for the match against Italy, entering in the final 23 minutes as Albania suffered another defeat. On 12 June 2017, in the match against Israel at Sammy Ofer Stadium, Sadiku returned to the starting lineup after nine months to score twice in the first half, both long-range strikes, as Albania got their revenge on Israel with a 3–0 away victory.

On 31 January 2018, in the deadline day, Sadiku was signed by Levante of La Liga for an undisclosed fee. The player signed a contract until June 2020. After several weeks sidelined due to knee injury, Sadiku made his debut for the club on 26 February by starting in the 0–2 loss to Real Betis. By doing so, he became only the second Albanian ever, the first being Valdet Rama, to play in La Liga. On 4 March, in the final minutes of the first half of the match against Espanyol, Sadiku suffered a head to head clash with goalkeeper Diego López; he was replaced at half time while López was sent to hospital. Sadiku then underwent surgery on his nose.

He concluded the second part of 2017–18 season by making only six league appearances, scoring no goals in the process. In August 2018, Sadiku suffered a major injury in his left knee while playing in a friendly against Netherlands’ Heerenveen. He remained sidelined for the entire first part of 2018–19 season.

On 15 January 2019, Lugano announced to have reached an agreement with Levante for the acquisition of Sadiku, who signed until the end of 2018–19 campaign. The contract included a clause, in which the Spanish has the right to rebuy Sadiku in the next transfer window. Club president Enzo Renzetti expressed his delight for the transfer, stating: “I have personally spoke with the boy. He is very motivated and is waiting with impatience to join us.”

On 2 September 2019, Sadiku extended his contract with Levante until 2021, and was immediately loaned to Segunda División side Málaga CF.

On 14 March 2019, Sadiku received an invitation for the opening UEFA Euro 2020 qualifying matches against Turkey and Andorra, returning in the national team after one year. On 22 March, he played as a second-half substitute in the first game against Turkey at Loro Boriçi, recording his cap in 361 days. Three days later, new caretaker manager Ervin Bulku decided to start Sadiku in the second game against minnows Andorra; the striker scored in the 21st minute with the open net after benefiting from the wrong clearance of opposition goalkeeper Josep Gómes, paving way to a 3–0 win at Estadi Nacional. It was his 12th international goal, overtaking Hamdi Salihi to become Albania’s fourth all-time top scorer.