The club refused to disclose the fee although it is expected to have met the 7 million pounds release clause that had been in Ba's contract at St James' Park.
The 27-year-old was the Magpies' top scorer last season with 16 goals in all competitions, and was also leading the scoring charts this term, with 13 strikes to his name.
Commenting on the move, Ba told the club's official website: "It feels good to be here, I'm very happy and very proud.
He added, "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."
The Senegal international will wear the number 29 shirt for the Blues and will be eligible to feature in Saturday's FA Cup tie away to Southampton.