Ivory Coast international Eboue had been expected to leave the Gunners this summer after he struggled for first-team action last season while he was not handed a squad number ahead of the new campaign.
"Arsenal have agreed terms with Turkish side Galatasaray for the transfer of Emmanuel Eboue," a statement on the Premier League club's website read.
"Everyone at Arsenal thanks Manu for his contribution towards the club and wishes him the best of luck for the future."
Gala later confirmed the move on their official website.
Eboue has signed a four-year contract on a deal the Turkish club has claimed is initially worth 3.5million euros.
The 28-year-old's departure ends a six-year stay in north London after he joined from Belgian side Beveren in 2005.
Eboue found himself down the pecking order at Arsenal last season when he managed just 13 league appearances and his exit loomed likely as he remained out of favour in pre-season.
His departure comes a day after Cesc Fabregas completed his protracted move to Barcelona while Samir Nasri is also expected to leave before the transfer window ends.
Eboue made 216 appearances in all competitions for Arsenal and scored 13 goals.