The 26-year-old has been a pivotal part of the Canaries team since joining the club from Peterborough in January 2010. Scotland international Martin, who can play at right back or in the centre of defence, will remain at Carrow Road until 2015.
"It's brilliant. I'm extremely delighted, my family and I are really happy around here," He told Canaries Player.
"It's a pleasure and an honour to be playing for a club of this size and stature. The last three years have been brilliant, and hopefully the next three can be just as good.
"As soon as the club spoke about it [signing a new contract], it didn't take long to get sorted because I'm so happy here personally.
"We've got a great bunch of lads so I'm really pleased to get it sorted so early on. I can now come back in pre-season raring to go."
The news comes just a day after Hughton left Birmingham to take charge of Norwich - with the former Newcastle boss also signing a three-year contract.
"Having just been appointed as manager I'm delighted that one of my first actions is to offer Russ this new three-year deal," Hughton added. "He's had a fantastic couple of seasons here since joining the club in January 2010 and this new deal shows what's he's done for the club over that time.
"He's been an ever-present and has shown he's a versatile player playing at both right-back and in the centre last season.
"Russ deserves this new contract and I'm delighted that he will be here for the next three years."
Source: PA
Source: PA