Gibbs, 18, has put pen to paper on a professional contract that will run through to the summer of 2025.
Discussing his move to the Canaries, Gibbs told the Norwich website: "I am very, very excited. I am looking forward to starting my journey as soon as possible.
"It is a new step for me and for my career. I am looking to make the most of it, showcase my talent and hopefully I can help the club keep moving forward.
"I have seen young players in the past that have gone through the academy and into the first team. Norwich have a reputation for bringing through young players and I just want to be the next one to get into the first team and make things happen.
"I can see a clear pathway for me. Now I am just excited to get started, fulfil my potential and show everyone what I can do."
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