The Argentina international had fallen out of favour at St James' Park this season after suffering a number of injuries, making just two appearances.
However, he will link up with former Newcastle manager Chris Hughton at Carrow Road, as he seeks to help 15th-place Norwich climb the table.
He is in line to make his debut for the club against Hull City in the Premier League on Saturday.
Gutierrez told Norwich's official website: "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.
"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."
Gutierrez moved to St James' Park in 2008 from Real Mallorca but suffered relegation in his first season at the club.
After helping Newcastle bounce back as Championship winners in the next season, he had played a regular part in recent seasons before seeing his appearances limited this campaign.
Hughton added: "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.
"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."
