The Dutch winger was always likely to leave following relegation from the Barclays Premier League and has been in Turkey in recent days to finalise the switch.
He arrived at the Stadium of Light in the summer of 2015 with high hopes but ended up with just 16 starts to his name and spent most of last season on loan at Fenerbahce.
The 29-year-old will continue to play his football in Istanbul after Besiktas agreed an undisclosed fee with the Black Cats.
A brief statement from the club read: “Jeremain Lens has completed his move to Besiktas.
“The Dutchman joins the Turkish club after two years on Wearside, where he made 24 appearances for the Black Cats, netting four goals.”