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.