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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."

"I was expecting it to be quiet, but not that quiet. Even the homeless people were still asleep," Dean Saunderson said of his expedition to capture a unique side of a city.
The 21-year-old photography student had been looking for inspiration for his project to make a portrait of his home town, Nottingham.
"I came across lots of images of abandoned towns and cities, completely untouched by humans for years, " he said.
"Knowing there isn't anywhere like that in the UK, I wondered if I could get close in some way."
Getting up before dawn on Christmas Day, he found a city given over to the birds and litter.
"It was a big shock. It felt so different, eerie. I kept checking over my shoulder.
"There was no one looking at you but it felt like there was no one looking out for you either - like anything could happen to you and no one would know.
"It reminded me of those pictures of the city near Chernobyl."
His ambition is now to visit a truly deserted place and put together a photo essay chronicling its story.

Father-of-six Peter O'Brien, 51, and 41-year-old Mark Sim died after a blast in the basement of the Celsa Steel UK plant in Splott on November 18, 2015.
Five men were also injured in the incident.
"What happened a year ago was the most tragic event in our history," said Celsa managing director Luis Sanz
"And our thoughts remain with their loved ones.
"We will be holding two minutes' silence to pay tribute to Mark Sim and Peter O'Brien," .
The then Prime Minister David Cameron tweeted his support to "those affected" by the explosion at Celsa's rod and bar mill, while Wales' First Minister Carwyn Jones said he was "deeply saddened" by the deaths.
More than 10 fire engines and ambulances attended the incident around 10:30 on November 18, 2015, while the air ambulance was also deployed.
Mr O'Brien, who lived in the Llanishen area of Cardiff with his wife Marie, played rugby and baseball for St Peter's RFC and more than 1,000 people attended his funeral.
Mr Sim, who lived in Caldicot in Monmouthshire with his wife Sam and their two children, was a fan of his home-town football club Newcastle United and played for his local darts team.
"We have been very moved by the levels of support we have received throughout Cardiff, Wales and the UK," added Mr Sanz.
"On behalf of everyone at the company, I want to say thank you for the kindness we have received.
"We continue to work closely with the authorities to establish the causes and learn lessons.
"The safety of employees is our absolute number one priority and we are deeply committed to the community here in Splott."
Norwich City have completed the signing of 23-year-old Leeds captain Jonny Howson for an undisclosed fee.
[NEXT_CONCEPT]
Inspired by pictures of deserted cities such as Pripyat, which was vacated in the fallout of the Chernobyl nuclear disaster, a photographer has been trying to capture quiet streets closer to home - starting with Nottingham on Christmas morning.
[NEXT_CONCEPT]
Steelworkers will observe two minutes silence on Friday to remember two colleagues killed in an explosion at a Cardiff plant a year ago.