The US star, who joined Schalke in 2007, has been told he has no future in Gelsenkirchen and wrote "Thanks for the wonderful years at Schalke, the fans will always be in my heart" on his Twitter account.
He later tweeted a picture of himself in a black-and-white Besiktas shirt, saying: "With pride and honor I will wear the black eagle jersey. Thanks to be part of this family. I can't wait to Start !!!"
Jones made three friendly appearances for Germany in 2008 before switching to play for the USA and has made 38 appearances for the Stars and Stripes since 2010.