Ba, 27, who has scored 13 league goals for The Magpies this season, will be eligible for selection for Saturday's FA Cup match at Southampton and the Capital One Cup semi-final against Swansea.
"It feels good to be here, I'm very happy and very proud," Ba was quoted as saying in Chelsea's official club website.
"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 said
"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," he added.
The Senegal international was a major transfer target for top Premier League clubs but Chelsea activated a release clause believed to be around £7 million and will earn nearly £80,000-a-week in wages.
Ba, who moved from West Ham United to Newcastle in 2011, comes in for Daniel Sturridge, who recently completed £12 million move to Liverpool.
The signing of Ba will lessen the burden on sole striker Fernando Torres who has scored 14 goals so far this season out of which only seven have been scored in the league.