Roma posted an image of the 28-year-old posing with a club scarf on Twitter on Sunday after he flew in for a medical, which is expected to take place on Monday.
Lyon have already confirmed the Serie A side have agreed a deal to sign Gonalons, who only has a year left on his contract, for a bargain €5m fee.
Gonalons has spent his entire career with Lyon and has seven caps for France, although he has not represented Les Bleus for two years.
Once confirmed, the midfielder's signing will add to those of Rick Karsdorp, Hector Moreno and Lorenzo Pellegrini under new sporting director Monchi.
In a busy off-season, the club have also recouped huge fees from Liverpool and Zenit for Mohamed Salah and Leandro Paredes respectively, while Antonio Rudiger is being heavily linked with a move to Chelsea.
Roma president James Pallotta has criticised the club's fans for a perceived "lack of faith" in their ambitions after the high-profile departures were questioned.