The 19-year-old has signed a four-year contract with the option for a further 12 months after impressing for the club whilst on loan for half of the season after arriving on Carrow Road on transfer deadline day in February. This move comes despite the side not having a head coach after sacking Johannes Hoff Thorup as the side looks to build a squad fit for a promotion race.
Speaking to the club website, Wright opened up on the move and why he decided that his future was at Norwich and not at City under manager Pep Guardiola.
"I'm really excited, this is what I wanted when I moved here. The last couple of months that I've spent here have cemented my feelings towards the club.
"I've really enjoyed my time here and hopefully that journey can now continue."
Sporting director Ben Knapper, who was likely in charge of bringing Wright into the club, praised the young playmaker and revealed what he will bring to the side.
"Jacob has been fantastic since joining us back in January, and his impact and performances made this an easy decision for us to make.
"He has established himself as a key member of our group already, and his potential is huge. Not only is he a very talented player, he has big leadership qualities and we’re all excited to continue working with him to help him achieve his potential and support us in striving towards our goals as a club."