The 32-year-old Spaniard is out of contract at the end of the season after five seasons at Stamford Bridge.
And reports from Italy say Roma have agreed a two-year contract with an option of a third, worth €3.5m-per-season.
Head coach Paulo Fonseca personally called Pedro, getting a guarantee from the former Barcelona star.
The arrival of Pedro will give Fonseca a new option for the wings, but also a deputy for Edin Dzeko up front.
With Pedro tied up, the Giallorossi will now focus their efforts on keeping Henrikh Mkhitaryan (on loan from Arsenal) and Chris Smalling (on loan from Manchester United).
Roma also want another centre-forward to replace Nikola Kalinic, with Nahuel Bustos a top target.
Tottenham defender Jan Vertonghen, another free transfer option like Pedro, is also on the club’s radar.