Gervinho arrived in the Italian capital on Sunday ahead of a medical and is quoted by the Gazzetta dello Sport as saying: "I'm happy to be here, it was my dream."
The Ivorian arrived at Arsenal in July 2011 but his stay in North London has not been a success.
The 26-year-old, who joined for a reported fee of £10m from Lille, was sent off on his Premier League debut after tussling with Newcastle's Joey Barton.
He scored just four goals in 28 league matches that season, and last term he fell behind Lukas Podolski, Olivier Giroud and Theo Walcott in the pecking order.
He played in 26 games last season, 18 of them in the Premier League, predominantly off the bench.
But Roma chief Rudi Garcia was his boss at Lille and they now appear set to be reunited.
Arsenal boss Arsene Wenger confirmed on the club's official website that Gervinho was on his way out: "Gervinho, we are at the moment close to an agreement with a club where he should go."
And Gervinho's fellow striking misfit Marouane Chamakh could also be leaving the Emirates shortly.
Wenger said: "Chamakh might go somewhere, it will be decided in the next 48 hours."
The Moroccan has been linked with a move to Premier League new boy Crystal Palace.