The 33-year-old joins the Canaries from Huddersfield where he was previously head of football operations
Webber had been placed on garden leave by the Terriers two weeks ago after expressing a desire to leave, with City having identified him as their first choice for the role
The former Liverpool director of recruitment will lead the hunt for a new manager at Carrow Road after last month's sacking of Alex Neil and with the Canaries now 10th in the Sky Bet Championship
He told the club's official website: "In terms of the next stage of my career, the opportunity to come to a club the size of Norwich was something which I couldn't turn down
"The club are embracing how things are done in Europe, where it's been successful for a number of years.
"The attraction of having the remit to come in and massively affect the football department, from the tip of the iceberg with the first team right down to the academy, makes it an exciting challenge for myself.
"There's a real carte blanche to go and do it as I believe is right and you don't get many opportunities like that at big football clubs."
Webber will work with managing director Steve Stone after Norwich - who also considered Celtic's head of development scouting David Moss for the job - changed their structure and made the role of chief executive redundant following the exit of Jez Moxey in February
Webber moved to Huddersfield in 2015 and revamped their scouting operation, playing a large part in appointing David Wagner in November 2015
Wagner has since turned the Terriers into promotion contenders and they are third in the Championship after Wednesday's 3-0 win over Norwich
Canaries chairman Ed Balls added to the club's official site: "With an excellent track record and growing reputation in the game, he was the man we wanted to bring in once we identified the role as a crucial part of our new structure
"We're excited about the impact he will have as he leads all of our football operations and recruitment."
Source : PA