The Senegal international will become the second forward to leave the club this summer, following the departure of Samuel Eto’o, as Jose Mourinho revamps his striking force.
The 29-year-old revealed his excitement at the prospect of the reported £8m move, which will be finalised once the player successfully undergoes a medical.
"The interest shown by the fans and the new stadium project won me over," Ba said, speaking on Besiktas’ official website.
"I'm very happy to be here, all that is left is a few formalities, I will undergo a medical and sign the contract. I am excited to be here and can't wait to start playing.
"I want to showcase my talent to the fans as soon as possible, this is a huge club and I want to become a part of it.
"I want to thank the fans for their warm welcome and I am sure we are going to establish a great relationship."
Ba, who joined Chelsea in January 2013 from Newcastle, was greeted by hundreds of fans at Istanbul's Ataturk airport on Wednesday morning.
Besiktas president Fikret Orman admitted his club are delighted at the prospect of adding Ba – who will wear the number nine jersey – to their ranks.
"Ba is a player we all believe in, we put in a lot of time and effort to complete the transfer to the best of our interests," Orman said.
"The transfer is within our budget and we are delighted to have completed the move."
Mourinho will look to new signing Diego Costa to provide goals this season, along with Fernando Torres and Romelu Lukaku, who returns from a season-long loan at Everton.
Also on Wednesday, Chelsea announced they have reached an agreement with Atletico Madrid over a fee for 28-year-old Brazilian left-back Filipe Luis.