Lambert helped guide the Canaries to his second promotion following successful season in getting his side into the Premier League this term.
Speaking of his delight at signing a new deal, he said; "It's terrific for myself and Ian and Gary. We came here together and we've never indicated we wanted to leave at all. I've loved my two years at the club".
"I'm delighted everything has been sorted for the three of us and now we are working on bringing players into the club. We have to try and give the current group a hand, as I have always said.
The Scot joined Norwich in 2009 and under his management Norwich have gained promotion from League One and the Championship in successive seasons.
"We want to try and make this club the best it can possibly be. We'll try and do everything we can to get a foothold in the Premier League and to enjoy it.
"The fanbase here is tremendous and if you have got them behind you, then you have a chance."
