"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."
Former Netherlands defender Frank de Boer will take temporary charge at Ajax until the winter break begins on 24 December.
Ajax general manager Rik van den Boog released a detailed statement expressing his regret at Jol's departure.
"Let me be clear that I respect, and am saddened by, Martin Jol's leaving," said Van den Boog.
"Officially, we've been having weekly meetings but we spoke to each other frequently besides that.
"Sports performance-wise, things aren't going as well as they have previously and the question is can the tide be turned? That's a hard question to answer.
"I think that Martin's been struggling with the situation. Everyone has an opinion about Ajax. His job comes with enormous external pressure, and this pressure has been increasing.
"The fact that this has happened today doesn't take away from the fact that last season was a fantastic one for us."
Jol, former Southampton manager Alan Pardew and ex-Aston Villa boss Martin O'Neill are some of the names thought to be in the running to take over at Newcastle.
It is the second time this year that Jol has been linked with a return to the Premier League.
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