Weaver, 30, was released by Charlton recently following the cash-strapped South London club's relegation alongside the Canaries. He was displaced in the Addicks' goal by youngster Rob Elliott as the side spiralled towards League One, but had been the club's Player of the Season in 2008.
The ex-Mansfield man built his career with Manchester City as they climbed from League One, keeping a record 23 clean sheets in 1999.
Once talented enough to be England's under-21 goalkeeper, Weaver seems to fit the bill for Gunn as he looks to build a strong, hungry team of leaders. He has experience at the level at which Norwich now find themselves, and will be eager to prove that he has plenty of good years left in him.