Salah has signed a five-and-a-half year contract with Chelsea and will wear the number 15 shirt.
"I'm very happy to sign for Chelsea, such a big club in the world. I hope I can make the Chelsea supporters happy and have a good career at the club for many years to come," Salah said in a statement.
Liverpool were also keen to sign the 21-year-old who came to attention in England during last season's Europa League and Salah was a key figure in Basel's two Champions League group-stage wins over Chelsea in the current campaign.
Salah became Chelsea's second major signing of the January transfer window following the arrival of midfielder Nemanja Matic from Benfica. Spain midfielder Juan Mata has left Stamford Bridge to join Manchester United.
(Reporting by Mike Collett, editing by Ed Osmond)
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