Cooper takes charge after Enzo Maresca left the newly-promoted Foxes at the end of last season for Chelsea.
He takes charge after being sacked by Nottingham Forest last season.
Cooper , 44, has agreed a three-year contract at Leicester and said: "I am really excited and proud to be appointed Leicester City’s First Team Manager. This is a fantastic Club with a rich history and passionate supporters.
"I am excited to work with such a talented squad and I’m looking forward to the challenge of achieving our shared ambitions in the Premier League.”
Foxes chairman Aiyawatt Srivaddhanaprabha also said: “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.
“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.”