Hughton, whose sacking came as a shock to players and fans alike, said he was leaving the Magpies with his head held high.
“We have built on last season’s momentum following promotion back up to the Barclays Premier League and have produced some excellent results to see us sitting midway in the table at this stage of the season,” he said.
“I am immensely proud of my achievements with Newcastle and I enjoyed a fantastic relationship with the players, my staff and the supporters during my time as manager. I now wish them and the club all the very best for the future. The termination of my contract is now in the hands of the League Managers’ Association and I will therefore be making no further comment at this stage.”
Newcastle are said to have fired Hughton because they are seeking a more experienced manager.
Meanwhile, Ajax confirmed Jol had left by mutual consent, with the Dutchman citing criticism of the club stemming from inflated expectations.
“The amount of criticism that the club has had to endure daily has led to unrest in the club and among players,” he said.
“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.”