The 30-year-old effectively took his leave of the Magpies over the weekend, when he posted a series of farewell messages on his personal Twitter account suggesting that his time at the club was over.
And he will now link-up once again with Canaries boss Chris Hughton, who was in charge at St James' Park between June 2009 and December 2010 as he led the Magpies out of the Championship and back into the top flight.
Norwich are certainly in need of reinforcements as they look to pull clear of trouble, with the Canaries in 15th place but only two points ahead of 18th-placed Cardiff after no wins in the last six league matches.
Argentina international Gutierrez, who joined Newcastle from Real Mallorca during the summer of 2008, figured only twice for Alan Pardew's side this season, and hopes he can make an instant impact with chance of regular football at Carrow Road.
''It is an opportunity for me to get back in the game and to try and do my best for the team,'' he said on the club's official website, www.canaries.co.uk.
''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 is a tough league, all the games are difficult, but we have a good opportunity.''
Hughton is in no doubt Gutierrez's Premier League know-how can benefit his squad in the challenges ahead.
''Jonas is somebody that will certainly bring experience - he has played close to 200 games for Newcastle, so he knows the Premier League very well," said Hughton, whose side take on Fulham at Craven Cottage in their FA Cup third-round replay on Tuesday night.
''He has been in England for five years, so there won't be that settling in period that you would have with some other players, and that is 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.''
The Canaries have no fresh injury problems ahead of the trip to west London, for which Hughton confirmed he would again utilise his squad as they look to secure a televised fourth-round tie away to Sheffield United.
''We know what awaits us in the next round and that would give us that little lift, irrespective of the competition," said Hughton.
''Firstly we have to get through and we found to our detriment last season (against Luton) it is not always the fancied team who go through.
''I wouldn't see an away tie at Sheffield United as anything but a difficult game, so we need to make sure we put ourselves in a position to get through."
Norwich's 18-year-old winger Josh Murphy could be handed another chance to impress, having started the first tie and was replaced by his twin brother Jacob late in the second half.
Hughton said: ''Josh is a young lad and maturing well.
''Fulham would have done their research for the first time, but they will definitely know him a little bit better now.''