The United States international made 109 appearances for the Premier League side, scoring three goals and providing 11 assists during his time with the Magpies.
Newcastle coach Steve Bruce hinted that the American's departure was to make room for another signing.
"[DeAndre] is certainly playing for a huge club in Galatasaray, so I wish him the best of luck.
"He's a great pro and a great lad, and sometimes you have to make decisions.
"We had to let somebody out to bring somebody in. So, it could be a busy day for us, but we'll see."
Yedlin will be joined at Galatasaray by Gedson Fernandes and Mostafa Mohamed, who also signed for the Super Lig champions on deadline day.