The Senegal striker has signed a three-and-a-half-year contract after his move from Newcastle for an undisclosed fee. The London club had triggered a £7million release clause in his Magpies contract.
Ba, 27, who will be eligible for selection for Saturday's FA Cup third-round match at Southampton, will wear the number 29 shirt.
He told Chelsea's official website: "It feels good to be here, I'm very happy and very proud.
"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.
"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."
Ba is joint-third in the Premier League scorers table this season with 13 goals so far.
The transfer puts the seal on a stunning rise from the lower reaches of French football to the European champions.
Born in the suburbs of Paris, Ba played for Port Autonome du Havre, Montrouge and third division side Rouen before moving to Mouscron, in the Belgian top flight.
He then moved to Hoffenheim, helping them win promotion to the Bundesliga, and was signed by West Ham two years ago.
Newcastle swooped after the Hammers were relegated that season and Ba played a pivotal role as the Magpies finished fifth in the top flight last season.
Chelsea will not lose his services for the African Nations Cup later this month as Senegal have not qualified.