Yılmaz started his professional career in Antalyaspor, where he was promoted to senior team at the age of 16. He scored his first two goals at professional level in 2004–05 season against Karşıyaka at Izmir Alsancak Stadium on 29 August 2004. In same season, Yılmaz played at 29 league matches, scoring 8 goals, thus helping his team avoid relegation. He contributed to the success of the team’s promotion to the Süper Lig after finishing second in Division 1 in the 2005–06 season, scoring 9 goals in 24 matches. During his stint at Antalyaspor, Yılmaz played 70 league games and scored 17 leage goals in total.

Yılmaz joined Beşiktaş at 2006–07 summer transfer window. He made his Süper Lig debut on 6 August 2006 against Manisaspor, and scored his first goal against Konyaspor in a 3–1 win for Beşiktaş. He also scored against Trabzonspor. In his first season, he scored 5 goals in 30 league appearances as Beşiktaş finished the season on 2nd spot. In same season, he had 7 appearance at Turkish Cup, scoring once. Playing form of Yılmaz dropped dramatically during the 2007–08 season. In January 2008, Yılmaz joined Manisaspor as part of an exchange deal, and later to Fenerbahçe on 29 June 2008.

On 29 June 2008, Yılmaz was transferred to Fenerbahçe and was presented at a news conference wearing the number 7 shirt. On the contrary to his “promising youngster” image in Manisaspor and Beşiktaş, he had been a disappointment during his spell in Fenerbahçe, only playing six games and failing to score in the 2008–09 season.

In February 2010, Yılmaz joined Trabzonspor on a permanent deal. Following the arrival of Şenol Güneş as team manager, Yılmaz made his Trabzonspor debut on 15 February 2010, playing last 15 minutes against Bursaspor on a 1–1 draw. On 26 February 2013, he scored against his previous team Antalyaspor. Yılmaz played at Turkish Cup final where Trabzonspor defeated Fenerbahçe by 3–1, on 5 May 2010. Ten days later, Trabzonspor played against Fenerbahçe again in lask week of Süper Lig fixtures in which Yılmaz scored in 23rd minute, as parties shared points after a 1–1 draw, causing Fenerbahçe to jeopardise their title chances in contention with Bursaspor. Yılmaz became leading goalscorer of Trabzonspor with 19 goals in 30 league games and July 2011 he signed a new four-year contract with the club.

In July 2012, Yılmaz joined Galatasaray from Trabzonspor for €5m transfer fee, with a four-year-contract with an additional one-season-option. His contract was conprised of €2.3 million seasonal wage with a €20,000 bonus per-appearance.

On 2 September 2012, he scored his first goal for Galatasaray against Bursaspor, as the game finished 3–2, making it Galatasaray’s historic 1000th league win.

Yılmaz scored the only goal for Galatasaray as the game ended in a 1–1 home draw against Eskişehirspor. On 23 October 2012, he scored a goal from a header against CFR Cluj as the game ended in a 1–1 draw at third match-week in Group H of the 2012–13 UEFA Champions League group stage. On 28 October 2012, Yılmaz scored his 100th career goal, during a 3–0 win against Kayserispor, maintaining their position as league leaders.

On 7 November 2012, Burak netted a hat-trick in a 3–1 away win over CFR Cluj at Champions Leage, becoming the first Turkish player to score three goals in a Champions League game since Tuncay Şanlı. At Champions League group stage, he scored once again, this time against Manchester United in which Galatasaray won 1–0. Yılmaz finished group stage of the as top scorer with 6 goals in total 501 minutes played, ahead of Cristiano Ronaldo, who scored the same number of goals in 540 minutes. On 23 November 2013, Burak scored his 100th Süper Lig goal against Sivasspor in a 2–1 home win.

On 5 February 2016, Galatasaray announced the transfer of Yılmaz to Chinese Super League club Beijing Guoan for €8 million transfer fee. Trabzonspor was to receive €2 million from Galatasaray, following the transaction agreement.

On 2 August 2017, Yılmaz returned to Trabzonspor, for family reasons. He managed to score 23 goals in 25 matches at 2017–18 season.

Lille announced the arrival of Yılmaz on 1 August 2020. The parties agreed upon a two-season-long contract. Substituted with Jonathan David in 64th minute, Yılmaz made his Ligue 1 debut against Rennes at first week encounter of 2020–21 season, ended 1–1, held at Stade Pierre-Mauroy, on 22 August 2020. On week 6, Yılmaz scored his first league goal against Strasbourg as Lille beat their opponents with 3–0 final score, on 4 October 2020.