Pellegrini, 20, joins the Bianconeri for a fee of €22 million.
"I would like to wish Luca Pellegrini the best of luck," said Roma chief executive Guido Fienga.
"A player who has come through the academy here, we hope he has a bright future ahead of him."
Pellegrini made his debut for Roma in September 2018, going on to make six appearances in total for the first team.
In January he joined Cagliari on loan, playing for the Sardinian side for the remainder of the 2018-19 campaign.
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