Burton replaces Stuart Wardle, who was among a group of staff exits last month which included club legend Darren Huckerby leaving his Under-23s assistant coach role.
As head of medical and sports science at League One club Scunthorpe, Burton led his department to the League One Medical and Science Team of the Year award at last season’s Football Medical Association Awards.
Burton will begin his role on November 22. He has previously worked for England Athletics before moving into football at Nottingham Forest, Barnsley, Hull City, Queens Park Rangers and Peterborough United, and has degrees in sports science and physiotherapy.
A City statement describes Burton – who was a trainee at Mansfield Town before playing in non-league for clubs including Gainsborough Trinity – as having ‘a glowing reputation’.
Burton, speaking to Scunthorpe’s website, said: “I would like to thank the chairman, his family and Jim Rodwell for supporting me throughout my time here at Scunthorpe United, without their backing and guidance it would have not been possible to deliver the level of service that we have.”
He continued: “I would also like to thank the manager and his backroom staff for their support and all the staff behind the scenes and players I have worked with during the last three years, there are too many to mention but I have enjoyed working with you all!
“Finally, I would like to wish the chairman, manager and the players well for the rest of the season and I really hope you achieve promotion to the Championship!”
Scunthorpe’s chief executive, James Rodwell, added: “We would like to wish Chris all the best in his new role at Norwich City, and we thank him for his work over the past three years with us. Chris has been a most valued member of staff in his time here, whose efforts have been most appreciated.”