The Senegal international moves to the Istanbul club after struggling to establish himself as a regular at Stamford Bridge following his switch from Newcastle United in January 2013.
He made just 23 starts in all competitions at Chelsea but spoke of a desire to impress at his new club after completing his €6 million transfer.
"I've had a lot of positive feedback about Besiktas and Istanbul from my Senegalese friends in Turkey," he told the club's official website.
"I know what my coach Slaven Bilic expects from me and I am open to all sorts of competition.
"Since Besiktas fans like hard-working and spirited players, I will give everything I've got in order to not to disappoint them."
The highlight of his spell at Chelsea came as he scored the goal that put them through to the UEFA Champions League semi-finals last season, securing a 2-0 quarter-final second-leg win over Paris Saint-Germain as Jose Mourinho's men levelled the tie at 3-3 on aggregate to progress on away goals.
But, despite that pivotal contribution, Ba was unable to win Mourinho over and he will hope to have a bigger impact with Besiktas as they bid to better last term's third-place finish.
Ba scored 14 goals in 51 appearances for Chelsea.
