The Egypt winger joined the Florence club on loan until the end of the season on Monday, with Juan Cuadrado moving in the opposition direction on a full-time basis.
Fiorentina have the option to make the move permanent, and Salah has designs on becoming a regular for Vincenzo Montella's men after making just eight appearances in all competitions for Chelsea this season.
"I am truly happy to be here," Salah told Fiorentina's official television channel. "I really hope this is a step forward in my career.
"I know that my move to Fiorentina has generated a lot of interest in Egypt and I hope I can do well and help the team succeed.
"I watched Fiorentina's game at Roma [the Coppa Italia quarter-final win] and I really like the team. I can't wait to get started."
Salah could make his debut for the Serie A club against Atalanta on Sunday.
