Chelsea Club, which did not disclose the financial details of the transfer, announced that 27-year-old Sterling signed a 5-year contract.
It was claimed in the British press that the transfer took place with a transfer fee of 50 million pounds.
Starting his professional career at Liverpool, Sterling signed with Manchester City in 2015 for £49m.
The English footballer, who took part in 337 matches with Manchester City, where he was the champion of the Premier League 4 times, scored 131 goals.