The five-time France international, last capped in a friendly against Paraguay in June 2014, arrived in the Italian capital on Friday for a medical, with Roma announcing the official completion of the deal a day later.
Grenier moves to Serie A until the end of the season, when Roma will have an option to make the switch permanent.
The 26-year-old attacking midfielder had fallen out of favour at Lyon, where he made just four substitute appearances in Ligue 1 this season.
Grenier has been with Lyon for his entire professional career, making his debut in September 2009.
Roma travel to Sampdoria in Serie A on Sunday.