INEOS already owns Swiss Challenge League side Lausanne, which it acquired in November 2017, while in March it bought the UCI World Tour cycling outfit formerly known as Team Sky.
The company was named as Nice's main sponsor for the 2019-20 season and has now bought the club, with Ratcliffe pledging to make "measured investment".
In a statement on Nice's official website, INEOS president Ratcliffe said: "With some sensible, measured investment, we want to establish Nice as a team that competes in European club competition on a regular basis. And importantly, sustain it.
"Nice has a great history and tradition, with a passionate fan base whom will play an important role in our journey.
"We made some mistakes at Lausanne, but we are fast learners. These have been rectified and we are already seeing the benefits.
"Clubs need to be successful off the pitch, as well as on it, and Nice will be no different, as we look to take the club from strength to strength in all aspects over the coming years."
Nice, coached by Patrick Vieira, have started the season in fine form, winning their first two Ligue 1 games.