Ba, 27, has moved to Stamford Bridge after the London club triggered a release clause in his Newcastle contract to the value of around £7.5 million.
The Senegal international, who has only been outscored by Robin van Persie and Wayne Rooney since moving to the Premier League in January 2011, is eligible to play in Saturday's FA Cup third-round tie against Southampton.
"It feels good to be here, I'm very happy and very proud," Ba said.
"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."
Ba replaces Daniel Sturridge in the Chelsea squad after the England international joined Liverpool in a £12 million deal earlier in the week.
He leaves Newcastle having scored 29 goals in 54 Premier League games for the club following a free transfer move from West Ham in June 2011.
Ba, who joined West Ham from German club Hoffenheim, scored seven times in 12 league games for the Hammers prior to their relegation.