Ba joins the European champions for an undisclosed fee, believed to match the £7.5m release clause in his contract at Newcastle.
The striker, who scored 29 goals in 54 league appearances during his time on Tyneside, will wear the No 29 shirt at Stamford Bridge.
He told the Chelsea website: "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.
"This club is at another level - it isn't West Ham or Newcastle. They are both big clubs with a strong history, but Chelsea is Chelsea and you cannot compare.
"It will be easier with world-class players around, who make the football look so easy."
Chelsea's interim manager Rafa Benitez said: "He gives us a different option up front. We are very happy with this signing. He can pass, he's good in the air, has good movement and can score goals."