The 54-year-old has been strongly linked with the job as new manager of Premier League side Newcastle United.
“With pain in my heart I say goodbye to this wonderful club,” said Jol.
“We started something last summer that I would have finished but I have come to realise that the expectations after last season were too high.
“We cannot meet such expectations. The amount of criticism that the club has had to endure daily has led to unrest in the club and among players.
“I take this decision consciously before AC Milan v Ajax is played. The coming weeks are very important and I sincerely hope that something happens in the squad to make it in the short term a winning team.”
Ajax legend Frank de Boer will take temporary charge of the club until the winter break begins later this month.
