The German-born Jones joined Schalke in 2007 and also played on loan at Blackburn Rovers in 2011 before returning.
"We are happy he has found a new club where he can meet his goals for the year," said Schalke sports director Horst Heldt in a statement.
"He can set the foundations for a good World Cup in Brazil with good performances and a lot of matches at Besiktas."
He did not give any details on the player's new contract.
The rugged 32-year-old midfielder, known for his physical game, had a contract with the German club until the end of the season but was out of favour in recent months.
Schalke face Real Madrid in the Champions League round of 16 next month.