Howson, a former England U-21 international, is now set to thrash out personal terms with the Norfolk club, who will in turn seek assurances over the player's fitness as the midfielder has been out since December with a knee injury.
Leeds were reluctant sellers of their captain, but felt given the 23-year-old's current deal was set to expire in the summer, they had to allow the move to happen, with a reported £2million fee.
"The player only has six months of his current contract remaining and has expressed a desire to play Premier League football at the earliest opportunity," the npower Championship club said in a statement.
"The club has been in discussions with the player about a new contract at Elland Road for more than 12 months, but he has been steadfast in his position that he would like the opportunity to play Premier League football.
"On that basis Jonny hasn't felt in a position to commit himself to Leeds United at this moment in time.
"The player would be able to leave on a free transfer at the end of his current contract.
"While accepting the offer on Tuesday the player has still to agree terms with Norwich and we are disappointed the matter has become public at this stage."
Norwich moved for former Leeds midfielder Bradley Johnson in the summer when he was a free agent after rejecting the offer of a new deal and allowing his contract to run down.
As with the signing of Johnson, 24, the transfer will be something of a gamble for Lambert - who has masterminded back-to-back promotions from League One after taking over at Carrow Road.