The Jamaica international underwent a medical in Italy on Tuesday, with the move then confirmed on Wednesday morning.
Villa will receive a loan fee of around £1.7million for Bailey, with Roma having an option to make the deal permanent for around £19m.
Bailey has made 144 appearances and scored 22 goals since joining Villa from Bayer Leverkusen for £25m four years ago.
But other than the 2023-24 season, when he played a key role in helping the club qualify for the Champions League, he has struggled for consistency.
Bailey scored only twice last season and a move this summer had been anticipated, with the player leaving the Villa Park pitch in tears following the final home match of the campaign.
Yet despite interest from Saudi Arabia, a firm offer to buy him permanently never arrived and Villa have now settled for a loan departure.
Roma will pay Bailey’s wages in full, freeing up space on Villa’s wage bill.
He becomes the third player to leave in the space of four days after Jacob Ramsey moved to Newcastle for a guaranteed £39m and Leander Dendoncker joined Real Oviedo on a free transfer.