Manager Jose Mourinho confirmed the signing prior to his side’s FA Cup fourth round victory over Stoke City at Stamford Bridge on Sunday.
The exact fee for Salah has not been revealed, although sources claim it is in the region of £15million, with some reports suggesting it could rise to as much as £20million.
The 21-year-old has signed a five-and-a-half-year deal with the club, and will wear the number 15 shirt.
Speaking to the club’s official website, Salah said: “I’m very happy to sign for such a big club. I hope I can make the Chelsea supporters happy.”
Salah has become Chelsea’s third signing of the January transfer window, following the captures of Bertrand Traore and Nemanja Matic.
He is set to offer Jose Mourinho further attacking options, following the departures of Kevin De Bruyne and Juan Mata.
Speaking on Friday, Mourinho revealed his admiration for the winger, who has managed 17 goals in 27 appearances for his country.
“We like the fact that he can play the same way our attacking players do, which is players with adaptability, to play right, left, or behind the striker,” Mourinho said.
“He’s young, he’s fast, he’s creative, he’s enthusiastic. When we analysed him he looks the kind of humble personality on the pitch, ready to work for the team and to work and to adapt himself to a new life.”
The news is set to come as a major blow to Liverpool boss Brendan Rodgers, who had reportedly made Salah his top priority signing this month.