According to various reports, the player is likely to cost around €40 million.
Chelsea have confirmed the transfer on their official website and Abraham will be hoping to kick start his career with regular football in Italy now.
Roma needed to sign a reliable goal scorer after the departure of Edin Dzeko and the 23-year-old Englishman could prove to be a superb long term acquisition for the Serie A side.
The player has been handed the number nine shirt at the Italian club.
Having completed his move to Roma, the player said: “Roma is a club that deserves to be fighting for trophies … 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.”
Abraham has shown his talent in England despite having limited opportunities and he leaves Chelsea having scored 30 goals in 82 appearances for them at the senior level.
He was also a part of the squad that won the Champions League and the UEFA Super Cup this year.
The 23-year-old needs to play regular first-team football in order to continue his development and fulfil his potential.
A move to Roma has come at the right time for him and he needed to leave Stamford Bridge for his own benefit.
It will be interesting to see if the player can hold down a regular starting berth under Jose Mourinho now.