The 23-year-old arrives in the Italian capital as a replacement for Edin Dzeko, who has joined Inter Milan.
Abraham fell down the pecking order at Chelsea after the club re-signed Romelu Lukaku from Inter Milan.
The former Swansea City loanee was Chelsea’s joint top scorer last season with 12 goals but had limited game time since Thomas Tuchel took over from Frank Lampard in January.
"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."
Tiago Pinto, Roma's general manager, added: "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.
"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."
Chelsea have included a buy-back option in Abraham’s contract with Roma which comes into effect in the summer of 2023 for £68m.
Abraham came through the youth ranks at Chelsea and has previously spent loan spells at Swansea City, Bristol City and Aston Villa.
He returned to Chelsea at the start of the 2019/2020 season and struck 18 goals in 47 appearances in all competitions.
Abraham has won six caps for the England national team but was not part of their EURO 2020 squad.
Roma, who are now managed by former Chelsea, Real Madrid, Inter Milan and Manchester United manager Jose Mourinho, will start their Serie A campaign at home to Fiorentina on August 22.
