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The midfielder agreed personal terms with the Canaries this week and, having passed his medical, he has penned a three-and-a-half-year deal.
"He can add goals to our midfield, which I think we need," said Norwich manager Paul Lambert.
"He'll get better as a player the higher the level he goes up. If he does that he'll be a great player for us."
Former England Under-21 international Howson, a product of the Leeds academy, has made almost 200 appearances since his debut in 2006, but his contract was due to expire in the summer.
He has featured 22 times for his home town club this season, although he has not played since picking up a knee injury in the 2-0 win over Millwall at the beginning of December.
Meanwhile, Lambert has outlined a back injury as the reason for terminating the season-long loan of Manchester United defender Ritchie de Laet five months early.
The 23-year-old Belgian has played seven times for the Canaries, but has not featured since the 2-0 Premier League loss to Tottenham on 27 December.
"Ritchie's done great for us," said Lambert. "But he has a back injury which was keeping him out for periods of time."
Norwich City have completed the signing of 23-year-old Leeds captain Jonny Howson for an undisclosed fee.