The former Preston North End man has settled in well at Carrow Road during his loan spell, barring a couple of controversial incidents. Etuhu was involved in a spitting row at the end of his debut against Luton, and ended his association with the Lillywhites a day after his challenge broke the leg of North End forward Adam Nowland.
"I'm just very pleased this has gone through," said the former Manchester City man. "Now I just want to get on with playing football for Norwich City."
"I'm still getting my fitness back and getting used to the way my team-mates play," added Etuhu, "but I'm sure it's the right move and I'm looking forward to working full-time under Nigel Worthington."
Worthington echoed the sentiment, emphasising that he felt the club had got a good deal in capturing the 23-year-old for £450,000 on a three year deal.
"I'm delighted to have been able to get the player," said the manager. "He's a very useful acquisition at a very reasonable price when you consider he came very, very close to joining Everton at the start of the season for nearer £1million"
Etuhu will have a valuable role to play in the next few weeks as Youssef Safri heads off to Egypt to play for Morocco in the African Nations Cup.