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.
Gutierrez will link-up once again with Norwich manager 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 the relegation zone, with the Canaries in 15th place but only two points ahead of 18th-placed Cardiff.
Hughton feels Gutierrez's Premier League experience can benefit his squad in the fight to secure top-flight survival.
He said on the club's official website, www.canaries.co.uk, following confirmation of the move: "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.
"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."
Argentina international Gutierrez joined Newcastle from Real Mallorca during the summer of 2008, when he signed a five-year contract.
He has made 195 appearances for the club and scored 11 goals, although has figured only twice this season, starting the 4-0 defeat by Manchester City on the opening weekend of the campaign and then coming on as a substitute in the 2-1 Premier League victory at Cardiff on October 5.
Gutierrez hopes he can make an instant impact 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.
"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."
Norwich are in action on Tuesday night with a trip to Craven Cottage for their FA Cup third-round replay against Fulham.
The Canaries have no fresh injury problems ahead of the match, for which Hughton confirmed he would again utilise his squad as they look to secure a live fourth-round tie away to Sheffield United.
Hughton said at a press conference: "I am very keen to use the squad. We felt we should have finished the (first) game off at Carrow Road.
"We know what awaits us in the next round and that would give us that little lift, irrespective of the competition.
"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.
"The only thing we don't know is what team Fulham put out because they obviously made quite a few changes from the previous league game (for the first tie)."
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: "He is certainly in the squad and I thought he was excellent in the first game. He 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."
Despite the focus on getting through to the fourth round, Hughton accepts Norwich's priority must always be top-flight survival.
"The morale here is still good, but we are very conscious of how competitive the Premier League is," said Hughton, whose side have not won for six league games following the 2-0 defeat at Everton.
"We are a point behind Swansea, who have had really good periods this season.
"We know it is closing up (at the bottom of the table) and the only way to get away from that is to win games."