The restaurant chain, with more than 900 outlets around the world, will be taken over by Sentinel Capital Partners and TriArtisan Capital Partners.
The terms of the purchase were not disclosed, but reports before the deal was announced put the value of the group at between $800m and $900m.
Sentinel will be TGI Fridays’ majority shareholder. The US private equity group already owns several dining chains in America including Newk’s Eatery, 223 Pizza Hut outlets in Los Angeles and a franchisee of Taco Bell.
Carlson, which operates Radisson hotels, started considering options for TGI Fridays back in November.
It said yesterday that the disposal of the chain “frees up resources that the company can deploy to focus on and accelerate the growth of its hotel and travel businesses”.