Having come through the youth ranks of Chelsea, Abraham contributed 30 goals in 82 competitive appearances at Stamford bridge.
"Abraham, 23, joins the club from Premier League side Chelsea--with whom he won the Champions League earlier this year--for a fee of 40 million euros," Roma announced in a statement.
"The overall transfer agreement also includes a number of performance-related clauses, based on the achievements of both the player and the club. Chelsea will also retain the right to a percentage of any future transfer fee involving the striker," it added.
After introducing Abraham, Rome has completed a merry-go-round with Chelsea and Inter Milan, as the Blues splashed out a club-record fee of 97.5 million pounds to sign back Romelu Lukaku from Inter, while the Nerazzurri brought Edin Dzeko from the Giallorossi as a replacement.
Abraham will wear the No. 9 shirt in the upcoming new Serie A season.