Ange Postecoglou's former assistant Papas coached the Jets in 52 games (16-10-26) over two seasons without making finals. He was contracted for next season but has now departed in search of an overseas opportunity.
"Over the past month Arthur has been transparent with the club that he was considering a return to working abroad," executive chairman Shane Mattiske said in a statement.
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"This has now been confirmed and although we are disappointed to see him depart, we respect his wishes."
Papas had clearly been frustrated by the club's almost three-year ownership limbo.
The Jets have been under the control of a consortium made up of several fellow A-Leagues clubs after previous owner Martin Lee was stripped of the licence in January 2021 for failing to inject any money into the club or pay off debts. There have been talks about potential new owners over the years, but no official offers have eventuated.
"I don't think the most important part is who's the coach, who's the players, the most important part is getting some stability into this club," he told reporters on April 29, after Newcastle's 2-0 loss to Sydney FC.
"I've been very clear that I'm very grateful and the club and the community should be very grateful to the ownership group that are currently in charge but it's bordering on three years now, I think.
"It's not easy to sell a club and also you don't want to lose a club because that's the threat. If you don't have ownership, you'll lose the whole club.
"Ultimately, I think if we're going to look for a signing in the offseason, I think that's the biggest signing we can make."
The Jets were confident of appointing a new coach quickly.
Newcastle face Melbourne Victory on July 17 in the Australia Cup playoff in Darwin.
"Whilst the departure of Arthur has only just been confirmed, we have been aware of the potential of a change and in the background have been considering a number of potential candidates," Mattiske said.
"We will now accelerate and close discussions with the aim of minimising the impact on team preparations."