The Greek defender has signed for the capital club on a free transfer from Perugia.
The 26-year-old fell out-of-favour at Perugia last season after rejecting a new deal at The Renato Curi.
Dellas was forced to spend the last six months of last season on the sidelines and only played eight games in the whole campaign.
The former Sheffield United ace is excited at the opportunity of playing for Roma.
"I'm very happy and this is a massive opportunity for me," said Dellas. "Roma are an important club and I'm very motivated to do well.
"I still haven't had the chance to speak with coach Fabio Capello yet but it is a real honour to be able to work with him."
Meanwhile Roma also unveiled three other signing, with Pep Guardiola, Luigi Sartor and Davide Bombardini all being presented along with Dellas at a press conference.