The 30-year-old is poised to join the Giallorossi until the end of the season with an option to make his transfer to the Serie A side permanent this summer.
Bastos, who was also a target of Napoli, would link back up with his former Lille coach Rudi Garcia at Roma.
"I am very happy to be here," Bastos said to Gazzetta dello Sport. "Forza Roma!"
Bastos can play as a European as he holds a French passport. He could make his Serie A debut at Hellas Verona this weekend.