A statement issued by the club on Thursday afternoon said they were "shocked and disappointed" by his decision but that his resignation was "reluctantly accepted" by chairman Andrea Radrizzani.
The former Swansea manager was only in charge at Elland Road for one season, after replacing Steve Evans last summer, but guided Leeds to a seventh-place finish in the Championship, missing out on the play-offs by five points.
After such a promising campaign, he was expected to sign a contract extension to remain with Leeds but Monk has decided against it.
His departure comes just a day after the controversial ownership of Massimo Cellino came to an end
In a statement, the club said: ''Leeds United can confirm that we have received Garry Monk's resignation from his role as first team manager.
''We are shocked and disappointed by Garry's decision but his resignation has been reluctantly accepted by chairman Andrea Radrizzani.
''Andrea made it clear to the media yesterday that his intention was to exercise the club's option to extend the manager's contract for another 12 months and immediately begin negotiations for a longer term deal.
''Mr Radrizzani has met with Garry twice since taking over at Elland Road earlier this week and during the second meeting yesterday it became clear that Garry was considering life beyond Leeds United, as at no time did Garry wish to discuss terms for a longer contract.
''Following that meeting yesterday Garry's agent requested that the option was not exercised and his resignation was received this morning.
''Whilst we are deeply saddened by Garry's decision, there is no individual bigger than our club and we will now begin a process to identify and appoint a new head coach to take the club to the next level.
''We thank Garry for his contribution during his time at Leeds United, we are disappointed that we could not continue on this journey together.''
Source : PA
Source: PA