The Ivorian was pointed in the direction of Turkey by his former manager after discovering that he would no longer find first-team football at the north London club
The Ivorian had become increasingly marginalised at the Gunners during the last campaign and recently opened up about the switch to Istanbul in the 2011 summer transfer window.
"Arsene Wenger told me it would be very hard for me to get a place in the first team, and because of that, I wanted to leave," Eboue was quoted as saying by Sabah.
"He told me that I should assess the Galatasaray offer.
"[Fatih] Terim declaring that he wanted me in a press conference made up my mind for me."
Eboue has made 24 Super Lig appearances since his move from Arsenal and his side currently sit nine points clear at the top of the table.