Leicester have been searching for a new boss after Enzo Maresca’s departure to Chelsea at the start of the month.
The club were disappointed the title-winning head coach left after just a season in charge, having guided them to an immediate return to the Premier League.
Maresca had been unhappy with problems he had spoken about but not detailed during the campaign, but any issues had been resolved following post-season talks and the club were looking forward to planning with the former Manchester City coach.
His departure did at least earn the club around £10m in compensation which will help with complying with profit and sustainability.
Leicester face the possibility of starting the season with a points deduction. The club were charged with breaching profit and sustainability rules in March and could face another punishment if they are not compliant by 30 June which may see them forced to sell players.
Cooper guided England Under-17s to victory at their World Cup in 2017 and also spent two years at Swansea, taking them to the play-off final in 2021 where they lost to Brentford.
He won the Championship play-offs with Forest a year later, ending the club’s 23-year exile from the top flight, having taken over when the club were bottom in September 2021.
Under him, Forest finished 16th in the Premier League in 2022-23 but he left the City Ground just before Christmas in the 2023-24 campaign with the club 17th in the table.