The Senegal international has largely been used from the bench since joining Chelsea from Newcastle United last year, and the arrival of Diego Costa at Stamford Bridge would limit his opportunities further.
Ba's Besiktas switch is yet to be formalised, but the 29-year-old is keen to make it happen.
"I feel so happy because Besiktas fans interest me a lot and the construction of the new stadium impressed me," he said. "I'm so excited to play for this club.
"I really want to play. I want to show my potential to everybody quickly.
"Besiktas is a big club and I want to be a part of this.
"The fans were very warm to me when I arrived here. I hope our close relationship will go on."
Ba made 19 Premier League appearances for Chelsea last year, scoring five goals, but was in the starting XI on just five occasions.
