United States international Jones, 32, has previously played for Eintracht Frankfurt, Bayer Leverkusen and Blackburn, and moves to Besiktas in a deal which gives the Turkish club the option to sign him permanently.
Schalke manager Horst Heldt has previously announced Jones would have no future at the Bundesliga club and they would not renew his contract.
"We're delighted that Jermaine has found himself a new club where he can realise his sporting ambitions this year," Heldt said.
"With good performances and plenty of appearances for Besiktas, he will be able to lay the foundations for a successful involvement in the World Cup in Brazil.
"We would not have been able to offer him that here in the second half of the season.
"We would like to thank him for his efforts in a Schalke shirt over the past seven years. As soon as the opportunity arises, we will give Jermaine a worthy send-off from Schalke.
"We wish him all the best for his professional and personal future."
Jones joined Schalke in 2007 from league rivals Eintracht Frankfurt while he spent the first half of 2011 on loan at Blackburn Rovers in the Premier League.
He made a total of 172 appearances for Schalke, scoring 10 goals, the last of which he scored in Schalke's 3-0 win over Stuttgart at the end of November.