The Argentina international has scored 11 goals in 195 appearances for Alan Pardew's side since moving to St James' Park in 2008.
But he has played only twice for the club this season and will now join up with former Newcastle boss Chris Hughton at Carrow Road.
Gutierrez was a key player for Hughton on Tyneside, helping the Magpies gain promotion back to the Premier League after they were relegated in 2009.
Norwich are 15th in the Premier League, just two points above the relegation zone, and Hughton was delighted to have Gutierrez at his disposal as he looks to guide City away from danger.
"He's somebody that will certainly bring experience - he's played close to 200 games for Newcastle so he knows the Premier League very well," Hughton told the club's official website.
"He's been in England for five years, so there won't be that settling in period that you would have with some other players.
"That's important, particularly in January when you need players that can go straight into the squad.
"Jonas can play on either flank and in a central position, so he's a very welcome addition and we look forward to working with him."
Gutierrez also admitted he was pleased to have a chance of playing on a more regular basis.
"I'm happy to be here. It's an opportunity for me to get back in the game and to try and do my best for the team," said the 30-year-old.
"Personally I want to do the right things on the pitch and win my place, and then for the team we want to finish as high as we can. It's a tough league, all the games are difficult, but we have a good opportunity."