The 26-year-old moves to England for an undisclosed fee, subject to international clearance, after three years in Ligue 1 with Rennes.
Tettey becomes manager Chris Hughton's seventh signing of the summer and, although clearance will not be received in time for the match at QPR on Saturday, Tettey will be present at Carrow Road as the Canaries look to put their shocking start to the season against Fulham last week behind them.
Tettey, who plays as a defensive midfielder, made a total of 82 appearances in all competitions for 'Les Rouges et Noirs' including 10 appearances in the Europa League last season.
Hughton told the club's official website: "I'm delighted to have Alexander on board and I firmly believe he will be a valuable asset for us.
"He's a very good player with international experience, and he's at a good age for us."
Although born in Accra, Ghana, Tettey is a naturalised citizen of Norway and started his career at the country's most successful team Rosenborg, with 22 league titles to their name.
Tettey joined the club in 2003 and eventually went on to captain the side in the absence of club legend Roar Strand, eventually spending six years with 'The Troll Kids'.
He made his senior debut in 2007 and went on to amass 89 appearances, including 12 in the Champions League, before leaving for Rennes in 2009.
He also scored an impressive 12 goals from the heart of midfield.
Tettey has represented Norway at under-18, 19 and 21 levels and has 14 full caps for the senior side making his debut in the 2-1 win over Argentina in August 2007.
Tettey's arrival comes ahead of the Canaries' first home game of the season with Hughton confident they can move forwards against QPR, who also lost 5-0 last week, beaten at home by Swansea.
New signings Sebastien Bassong and Javier Garrido - who has finally received international clearance on a season loan from Lazio - could make their debuts as the Norwich manager looks to get a first win under his belt.
"You can definitely use this as a positive, use this type of defeat to galvanise and hit home to everybody that you need to play well enough to win games," said Hughton.
"Of course, I would rather have not lost so heavily, to be able to go into the QPR match having say drawn at Fulham or even won there, but you have to use every circumstance to your benefit.
"The challenge now is just as difficult as I thought it would be two weeks ago - but it will be so for a group of teams.
"We can all be emotional about it, and it is not a nice period, but you bounce back from that."
Hughton continued: "We have watched it as a team, and gone through where we could have done better as a team, and that is always the best way.
"Sometimes you can learn more from a heavy defeat, but we also needed to close it down as quick as we can - we have had a good week's training so we now look forward to the next one."
As well as Tettey's arrival, a £1million move for Blackburn goalkeeper Mark Bunn is expected to provide back-up for England international John Ruddy.