The 28-year-old Norway international, who joined Norwich from Rennes in August 2012, has the option for another year.
Tettey has played in all seven of City's league games this season and has recently scored against both Watford and Brentford.
Norwich manager Neil Adams said: "I'm absolutely delighted Alex has extended his stay with us. He's had a fantastic start to the season and worked very hard in midfield with Bradley Johnson and there's no doubt he's a big, big player for us."
Tettey, who has scored four goals in 58 appearances for the club, said: "I'm delighted and happy that Norwich wants to keep me here and that we've been able to agree on a deal.
"Norwich as a place and as a club suits me very well. The project of getting us back to the Premier League is exciting.
"As people know we've started the season well and the club's desire to get back into the Premier League is something that is attractive to me."
Norwich top the Sky Bet Championship table after the 3-0 win over Brenford on Tuesday night, but Tettey has admitted he nearly punched a Bees player during the game.
"It was hard. I came very close to hitting Alan McCormack or someone," Tettey told BBC Radio Norfolk.
"They were really up for it and had players trying to wind us up, but it was good we kept our cool."
Brentford boss Mark Warburton complained that officials view him and his staff as "too polite", but that was not a compliment Tettey was willing to extend to his players.
The Norwegian added: "Someone made a tackle and they had to stitch my leg up in the first half. I had to keep my calm.
"I had Lewis Grabban grabbing me and telling me to carry on and deal with it after the game.
"I think that helped me. Because at that moment I was going nuts. But we won and we can go home with three points."