The Egypt international joined the Serie A club on loan until the end of the season on Monday, with Juan Cuadrado moving in the opposition direction on a full-time basis for €33 million.
Fiorentina have the option to make the move permanent and Salah is determined to become 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 and I really hope this is a step forward in my career," Salah, 22, told the Viola's official television channel.
"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.