The Blues have announced the capture of the forward for an undisclosed fee and he will be eligible for Saturday's FA Cup tie against fellow Premier League club Southampton
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.
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"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.