Ba has signed a three-and-a-half year contract and will wear the no. 29 shirt at Stamford Bridge.
Demba Ba said of his move from Newcastle to Chelsea: "It feels good to be here, I'm very happy and very proud.
"It was important for me, and for Newcastle, to get my future sorted and now we can move on. Now they have the whole month to buy someone and for me as well, the sooner the better. Now I am here I just need to get settled in.
"When the club who won the Champions League wants you, the decision is very easy. This club is massive and that's something that helped the decision a lot. It was not a hard one."