Europa Conference League winners Roma, who finished sixth in Serie A last season, announced last week they had signed Dybala after his contract with Juventus expired.
Jose Mourinho has also added 33-year-old former Manchester United midfielder Nemanja Matic to his squad this summer.
Dybala, 28, spent a trophy-laden seven years in Turin, after joining Juve from Palermo in 2015, but has been dogged by injuries over the last two seasons.
"Obviously I have experience after so many years at Juventus, a team that's used to winning and transmits that to you from the first day," he told reporters.
"So I will try to give my maximum even in the dressing room with my team, seeing as we're a young team, to bring that experience to help to win, help to be positive in the difficult moments there will be during the year".