Clarke, 18, has put pen to paper on a professional contract with the Canaries.
The midfielder arrives from recently promoted Peterborough United, where he made 11 senior appearances. Clarke made his first-team league debut for the Posh in September 2020 against Accrington Stanley at age 17.
Clarke told the club's website: “This is a great club and I feel absolutely delighted to sign here. I'm over the moon.
“Norwich have a reputation for the work they do with their younger players. They try to make a pathway for them and that really opened my eyes and grabbed my attention.
“The club also recently got promoted to the Premier League, so it feels like a no-brainer for me.
“I'd like to try to make a breakthrough to the senior team, I'd like to show all the fans, staff and players around me what I'm capable of and hopefully I can get a shirt."
Clarke will initially form part of the club's development and academy setup.