The 67-year-old Gasperini has signed a three-year contract with Roma after making Atalanta one of Italy's best clubs, including a European League win last year.
He replaces Claudio Ranieri, who is leaving after Roma's fifth-place finish in Serie A last season. Ranieri was present when Gasperini was presented and wished the new coach good luck.
Even Juventus was after Gasperini.
Roma's fifth-place finish meant the club missed the Champions League again. The team has not reached it since 2017.