Howson, a former England Under-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.
Many of the current squad have come up through the divisions with the Canaries, while summer additions Steve Morison, Anthony Pilkington and Elliott Bennett have all made a successful transition into the top flight.
Lambert, however, admitted he was unsure how many more times he could tap hungry talent from down the pyramid as he looked to keep Norwich in the Premier League following an impressive first half of the season which has left them ninth.
Goalkeeper John Ruddy believes the current group have already shown they have what it takes to last the distance.
"Over the Christmas period we had a couple of games, but we used the squad very well," Ruddy said in the Eastern Daily Press.
"It gave players a chance who had not played very much this season, they came in and did an unbelievable job.
"We have got more than enough in the squad, but if the gaffer needs to add to it he will.
"We will welcome them with open arms and they can help us stay in the league as well."
Norwich host Chelsea on Saturday, where Lambert is again expected to keep faith with centre-back pairing Daniel Ayala and Zak Whitbread.
Belgian defender Ritchie de Laet has, meanwhile, returned to Manchester United after his season-long loan deal was cancelled.
The 23-year-old has been hampered by a back injury, which limited his impact with the Canaries.
Lambert said: "We thank Sir Alex Ferguson for loaning him to us and wish Ritchie well for the future and hope he goes on to have a successful career at Manchester United."