Yildirim previously won the Super Lig with Bursaspor in 2010 – the first side outside the big four to win the league title in Turkey.
Bursaspor have lost a lot of blood over the summer. Şener Özbayraklı and last seasons goal king Fernandao joined Fenerbahçe, Enes Ünal moved to Manchester City and Batuhan Altıntaş was snapped up by HSV.
Last seasons manager Şenol Güneş also left the club and ended up joining rivals Beşiktaş.
Bursaspor are now coach by Ertuğrul Sağlam who coincidently was in charge of the side that won the league title back in 2010.
Yildirim spent last season on loan with Balıkesirspor who ended up getting relegated from top-tier football.
The 24-year-old Turkish international fell out of favour with Galatasaray fans and was booed in the recent friendly against Inter.
Galatasaray have brought in Lukas Podolski, Bilal Kısa, Jese Rodriguez and Jem Karacan over the transfer window.