Veretout will cost Roma a €1 million ($1.6 million) loan fee with the deal including an obligation for the Giallorossi to make the move permanent for €16 million ($25.8 million) next year.
The transfer for the 26-year-old also includes a potential €2 million ($3.2 million) of add-ons to be paid to Fiorentina.
Veretout, who has agreed a contract to 2024 with Roma, previously played for Nantes, Aston Villa and Saint-Etienne.
"I am very happy to play for this great club, with so many great players," Veretout said.
"I am looking forward to sharing a great new phase of my career with some fantastic team-mates."
Veretout is the latest new arrival for Roma, who have also signed Leonardo Spinazzola, Amadou Diawara, Bryan Cristante and Pau Lopez but allowed club legend Daniele De Rossi to depart.
"I am really pleased to be able to bring Jordan to the club,” Gianluca Petrachi, Roma's sporting director, said.
"From the very start of negotiations I recognised his eagerness to come here and wear the club's colours. I am certain that his desire and technical qualities will prove a vital part of the side we are building."