Leicester were disappointed that Maresca decided to leave the club after winning the league title.
The Foxes considered a number of replacements, including West Brom manager Carlos Corberan.
Cooper brings Premier League experience, having kept Forest in the top flight with a 16th-place finish following promotion in 2022.
He was very popular with Forest fans but was sacked midway through last season when the club were in 17th place in the table.
The former Forest manager led England’s Under-17 team to victory at the 2017 World Cup and also spent two years at Swansea, taking the team to the 2021 Championship play-off final where they lost to Brentford.
Cooper’s first competitive game as manager will be on August 19, when Leicester host Tottenham in the Premier League.
“We are delighted to welcome Steve to Leicester City. His vision for the team, including his ability to develop players and implement a dynamic style of play, is fully in line with our ambitions for the club,” said Leicester chairman Aiyawatt Srivaddhanaprabha.
“As a leader, he has the ability to build on the strong relationship that has been developed between our fans and our team, strengthening a bond that will be vital to the club’s re-establishment in the Premier League.”