Leicester were disappointed that Maresca opted to leave the club following their Championship title win.
The Foxes considered a number of replacements, including West Brom manager Carlos Corberan.
Cooper provides the Foxes with Premier League experience, having kept Forest in the top flight by finishing 16th following their promotion in 2022.
He was a popular figure with Forest supporters but he was sacked midway through last season, with the club 17th in the table.
The former Forest boss guided England’s Under-17s to victory at the 2017 World Cup and also spent two years at Swansea, taking them to the Championship play-off final in 2021 where they lost to Brentford.
Cooper’s first competitive fixture in charge will be on 19 August, 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 very much aligned with our aspirations for the club,” said Leicester chairman Aiyawatt Srivaddhanaprabha.
“As a leader, he has the ability to build on the strong relationship that has been forged between our fans and our team, strengthening a bond that will be vital to us re-establishing the club in the Premier League.”
