Abraham has signed a five-year contract with the Serie A club to fill the void left by Edin Dzeko's departure to Inter.
Chelsea will reportedly receive a further €5m in add-ons and have an option to re-sign the 23-year-old, who fell further down the pecking order when Romelu Lukaku returned to Stamford Bridge last week.
Arsenal were linked with Abraham, but he has opted to try and kickstart his career under Jose Mourinho in Rone.
"You can sense when a club really wants you – and Roma made their interest clear immediately," Abraham, who will wear the number nine shirt, told Roma's official website.
"Roma is a club that deserves to be fighting for titles and trophies. I've had the experience of winning major trophies and I want to be in those competitions again – so I want to help this team to achieve that and get to the level where Roma should be.
"It's a massive honour to be the number nine at this club and I just can't wait to get started and to help the team."
After scoring 15 Premier League goals for the Blues in the 2020-21 season when Frank Lampard was in charge, Abraham saw his opportunities diminish under Thomas Tuchel last term.
The 23-year-old started only three league fixtures following the appointment of Tuchel in late January, while he did not feature at all in the knockout stages of the Champions League as Chelsea went on to lift the trophy in Porto.
He also missed out on England's squad for Euro 2020, with Dominic Calvert-Lewin preferred by Gareth Southgate as a direct back-up to Harry Kane.
Abraham will be hoping to have similar success in Serie A as another England international, Chris Smalling, who rejuvanated his career with a loan switch to Roma in 2019-20, which was made permanent last year.