The 22-year-old only arrived at Stamford Bridge from Basel last January, but has struggled to make an impact under Jose Mourinho.
Salah will now spend the rest of the campaign in Serie A with La Viola, who sold Juan Cuadrado to the Blues just a matter of hours earlier.
The Colombia forward's transfer is likely to be the biggest deal of deadline day, joining for a fee which will reportedly rise to his £26.8m release clause. The move for Salah will help the void left by Cuadrado at Fiorentina, while striker Stipe Perica has also moved to Italy.