The npower Championship confirmed they had 'reluctantly' accepted an offer for the 23-year-old, whose deal at Elland Road expires in the summer.
A statement on the club's website read: "The club has reluctantly accepted the offer on the basis that 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."
Howson has been out of action since December because of a knee injury, and Leeds revealed their disappointment at not being able to tie the former England Under-21 international down on a longer deal.
"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," the statement continued.
"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 signed Bradley Johnson on a free transfer from Leeds in the summer after the midfielder's contract with the Yorkshire club had expired.