The loan fee was not disclosed but Italian media valued the deal at eight million euros, including bonuses.
The forward will be reunited with Roma manager Jose Mourinho, who worked with him at Chelsea and Manchester United.
"The welcome I've received from this club and its fans has excited me and given me even more motivation to give my all for my new team," Lukaku said.
"I recently got the opportunity to speak with the owners, and I was impressed by their ambition. Now we must work, be humble, and grow game by game. For my part, I can't wait to be available to my teammates both on and off the pitch."
Lukaku, who had a successful loan spell at Inter Milan last season, has reportedly agreed to a large wage cut.
Roma have one point from their first two Serie A matches this season and host AC Milan on Friday.