The USA international, whose contract was due to expire in the summer, travelled to Turkey over the weekend and has completed a permanent move to the Süper Lig club.
Yedlin joined the Magpies from Tottenham Hotspur in August 2016, scoring in his second appearance for the club in a 2-0 win at Derby County and establishing himself as a key part of United's Sky Bet Championship title-winning team.
The 27-year-old right-back scored twice more in a total of 125 appearances for the club.
Everyone at Newcastle United wishes him the best for the future.