Born in Rome, Pellegrini, who had suffered from arrhythmia as a youngster, joined the youth academy of local side Roma at the age of nine.

[5][6][7] Having previously represented the club in the UEFA Youth League, he was handed his senior debut at the age of 18 by manager Rudi Garcia on 22 March 2015, coming on as a second-half substitute for Salih Uçan in a 1–0 Serie A win over Cesena.

[9] In terms of the transfer agreement, Roma retained a buy-back-clause which afforded the club the opportunity to re-purchase Pellegrini at a future stage.

[15] On 30 June 2017, Roma exercised the buyback clause of €10 million, which was included in Pellegrini's transfer agreement with Sassuolo, to bring him back to Rome on a five-year deal.

He made his first appearance for the senior side in an 8–0 victory over San Marino in an unofficial friendly match on 31 May 2017, coming on as a half time substitute for Daniele Baselli.

[32] In June 2024, Pellegrini was included by manager Luciano Spalletti in Italy's squad for UEFA Euro 2024,[33] and was later assigned the number ten shirt.

A former central defender in his youth, he is also an effective ball-winner, which enables him to break down possession, while his vision and technical skills allow him subsequently to carry or distribute the ball and provide assists for his teammates.

His wide range of skills thus enable him to contribute at both ends of the pitch, and make him effective in linking both the defensive and offensive aspects of the game in a box-to-box role.