The 32-year-old made the move to Carrow Road in 2012, signing from Ligue 1 side Rennes for a reported fee of around £3m. He has gone on to make 177 appearances for the club across all competitions, scoring five goals.
In an interview with Norwich City TV, the Norway international said: “I'm very happy to have signed because since I've been here, I've enjoyed myself.
"It's been a couple of months where there has been a lot of thinking with my family so I'm pleased it is now done. Norwich is a family club and that suits me a lot.
"The coach's philosophy is very good. We have learned a lot from this season. Next season, we will be even better because everyone will know what he wants from us. Hopefully that will get us firing from the beginning of the season.”
Norwich City boss Daniel Farke added: “It's good news for the group, for the club and for Alex.
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"We want to keep our key players and Alex is 100 per cent one of our key players. We have a young group so need experienced players who are able to lead and help them develop.
"We want players who are desperate to play here and Alex has a strong identification with the club. I'm really happy he's signed a new contract."
Norwich currently sit in 12th place in the Championship, with their final fixture this Sunday away to fellow mid-table side Sheffield Wednesday.