The Senegal international moves to Stamford Bridge following an 18-month spell with Newcastle United, and has signed a three-and-a-half-year contract with the Blues.
He will be eligible for selection for tomorrow's FA Cup match at Southampton, and the Capital One Cup semi-final against Swansea, but cannot play for us in the Europa League this season having appeared in the competition for Newcastle. He will wear the no. 29 shirt.
'It feels good to be here, I'm very happy and very proud,' Ba says.
'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.'
Thus far, he has scored 13 Premier League goals this season.
He has scored four times for his country and becomes the first Senegalese player to join Chelsea.