The deal is now subject to the paperwork being approved by the relevant footballing authorities.
Canaries manager Paul Lambert believes that the 23-year-old will add goals to his midfield options.
"I think he has been brilliant for Leeds - how he has played but also being their captain brings its own demands. It's a fantastic club Leeds," Lambert told the club's official website.
"I think he can add goals to our midfield which I think we need and he can do that. He'll get better as a player the higher the level he goes up. If he does that and everything goes well, he'll be a great player for us."
Howson, who has signed a three-and-a-half-year contract, will wear the number 24 shirt for Norwich.