The club refused to disclose the fee although it is expected to have met the £7 million release clause that had been in Ba's contract at St James' Park.
The 27-year-old was the Magpies' top scorer last season with 16 goals in all competitions, and was also leading the scoring charts this term, with 13 strikes to his name.
|START WITH A BANG|
|10/3||Demba Ba is 10/3 with Bet365 to score first when Chelsea face Southampton on Saturday|
"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."
The Senegal international will wear the number 29 shirt for the Blues and will be eligible to feature in Saturday's FA Cup tie away to Southampton.