With this latest purchase 66-year-old Ratcliffe adds to a sports portfolio that already includes the former Sky cycling team and Swiss club Lausanne-Sport.
Ineos was given the all-clear to seal the deal with Nice's Sino-American owners by the French Competition Authority last week.
"It has been quite a long journey getting here, but it is unique, and we were determined to complete the purchase of the club," Ratcliffe, a Brexit backer based in Monaco, told the club's website.
"We have looked at a lot of clubs in the manner we look at businesses in INEOS -- for value and potential -- and Nice fulfils that criteria.
"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."