Abraham is expected to sign a five-year contract worth £4 million a year after tax.
Abraham lost his place in the Chelsea squad after German coach Thomas Tuchel replaced Frank Lampard.
With Romelu Lukaku's return to Chelsea, Abraham was expected to look elsewhere for more playing time and a move to Roma would be the best option as their regular striker Edin Dzeko edges close to Inter Milan.
Abraham's last inclusion in a Chelsea squad was when Tuchel added him to his team that faced Spanish LaLiga club Villarreal in the Super Cup final which the Blues won on penalties.
Roma have since been in talks to sign the England international as a replacement to Edin Dzeko, who has joined Serie A champions Inter Milan.
Abraham having become out of favour and craving for more first team opportunities is now close to completing his switch to Italy after Roma finalised talks between his representatives and Chelsea last week.
Reports are that Abraham's deal includes a buy-back clause set at £68 million which can only be triggered after the former Aston Villa forward has spent two seasons with the Giallorossi.
Abraham was with Chelsea's youth side during Jose Mourinho’s era but never made a senior debut before the Portuguese gaffer left the side.
The 23-year-old could have joined Arsenal after Mike Arteta's side showed interest in signing him but Chelsea's plan was to sell him to a foreign club.
Abraham managed to register 12 goals in all competitions for Chelsea last season.
Chelsea began their Premier League title challenge with a 3-0 victory over Patrick Viera's Crystal Palace at Stamford Bridge.
