The Italian side have agreed to pay an up front fee of €2.5 million and can buy the French full-back outright at the end of the season for an undisclosed fee, reportedly in excess of €15m.
The move sees Digne reunited with old Lille boss Rudi Garcia, with the manager handing the France international his first-team debut in 2011, while PSG are set to bring in Layvin Kurzawa as his replacement.
"I chose Rome because it is a historic club," Digne told the club's official website.
"The club is also in the Champions League and the fans are very welcoming, which is very important to me. I know that this city and club have all the ingredients to be successful."