The 23-year-old had fallen out of favour with current Chelsea manager Thomas Tuchel and has signed for the Serie A side on a five-year deal and will wear the No 9 shirt for the Giallorossi.
Abraham scored 30 goals in 82 appearances for the Premier League club after coming through the Blues academy and has also won six England senior caps, scoring once.
“You can sense when a club really wants you — and Roma made their interest clear immediately,” said Abraham.
“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 No 9 at this club and I just can’t wait to get started and to help the team.”
Abraham was a regular starter under former Chelsea manager Frank Lampard during the 2019-20 campaign — when he scored 15 goals in 34 Premier League games — but the arrival of Tuchel in January saw his chances limited. He scored just six goals in 22 league games last season.
The return of Romelu Lukaku in a £97.5m switch from Roma's Serie A rivals Inter Milan meant Abraham had fallen further down the pecking order at Stamford Bridge.
Chelsea director Marina Granovskaia said on the club website: “Tammy will always be welcomed back at Stamford Bridge as one of our own. We have all enjoyed watching his progress through our academy and into the first-team squad and are grateful for his contribution to our successes at senior and youth level.
“His many goals in a Chelsea shirt and, of course, his part in our Champions League triumph last season will never be forgotten. I’m sure all Chelsea supporters will join me in wishing Tammy a long and successful career.”
Now Abraham will be looking to get his career back on track under the guidance of Mourinho, who took over as Roma manager this summer.
“Despite still being very young, with a huge amount of potential to keep improving, Tammy has already played more than 200 games in his career and scored over 100 goals — and won a number of major trophies too,” Roma’s general manager Tiago Pinto said on the club’s website.
“Choosing to leave the Premier League, and the club he grew up at, demonstrates very clearly just how much he believes in this opportunity to develop his own game and show what he can do at Roma.
“Bringing in players that have such a hunger and desire to play for our club is hugely important in helping to build the identity and sense of belonging that is a fundamental part of our overall vision for this team.”