"We are shocked and disappointed by Garry's decision but his resignation has been reluctantly accepted by chairman Andrea Radrizzani," the club said in a statement on Thursday.
"Mr Radrizzani has met with Garry twice ... 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."
Monk issued a statement later on Thursday, saying: "My intention was always to remain at Leeds and I saw myself at this fantastic club for many years to come.
"However, ultimately no agreement could be reached.
"After discussions with the new owner, we have unfortunately been unable to agree a suitable way for us to all move forward together," added the 38-year-old.
The former Swansea City boss joined Leeds at the start of the season and guided them to seventh in the second-tier Championship, just missing out on a playoff spot.
Leeds are one of England's traditional giants, having won the top-flight title three times and been European Cup runners-up, but the Yorkshire club have had turbulent times on and off the pitch since losing their Premier League status in 2004.
(Reporting by Hardik Vyas in Bengaluru; Editing by David Goodman and Ken Ferris)
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