The Ivory Coast full-back left the Emirates Stadium for the Turkish outfit before the start of the current season after six years with the Gunners, making just 13 league appearances in his final top-flight campaign.
Talking to Turkish website Sabah, Eboue admitted that Wenger told him to consider the interest from the Istanbul based club and that his future manager’s determination to acquire him was tempting enough to make the move.
He said: "Arsene Wenger had told me that it would be very hard to get a place in the first team, and, therefore, I wanted to leave.
“He told me that I should assess the Galatasaray offer. [Fatih] Terim declaring that he wanted me in a press conference made my mind up.”
Terim, in his third tenure with the 17 time Super Lig champions, has been an inspirational figure for the 28-year-old and Eboue insists the coach has made his life easier at the club.
The Ivorian added: "Terim gave me confidence. I learn about him more every day. You can clearly see Terim’s passion over his job, football and club.
“That’s why fans adore Terim and his work. Turkish and foreign players united as a family in Galatasaray.
“This synergy is Terim’s success. At the beginning of season, I was not comfortable of my position in field."