Wigan Athletic legend parts company with Luton Town
Jones only took charge at Kenilworth Road last summer, ahead of the Hatters' return to the Championship.
Luton, most people's pre-season tips for relegation, stand six points adrift of safety with nine games still left to play.
But they had been in fine form before the season was postponed due to the Covid-19 pandemic.
His final game in charge, fittingly, was the 0-0 draw against Latics at the DW Stadium on March 7.
A Luton statement read: "Given the current circumstances affecting not only football but the world as whole, the club are taking an early move to restructure in order to reduce its cost base and to create efficiencies within the football department.
"As a result of amicable discussions, Graeme and the board of directors have agreed terms upon which he will leave his role with immediate effect.
"The board would like to place on record their thanks to Graeme for his efforts over the last 12 months.
"We wish him and his family well during these difficult times for everyone, and in his future career.
"Assistant manager Gary Brabin, first-team coach Inigo Idiakez and technical goalkeeping coach Imanol Etxeberria have also had their contracts terminated with immediate effect.
"We would like to thank all three for their service to the club and wish them all well for the future.
"When we have more concrete knowledge about the recommencement of the 2019-20 season or the start of 2020-21, we will then reconsider our position with regards to the football management structure.
"Meanwhile, applications for any of the positions will not be considered or reviewed at this time.
"In the interim period, chief recruitment officer Mick Harford will act as a relationship manager between the board, staff and the playing squad on football matters.
"The club will be making no further comment at this stage as everyone continues to battle with the challenges of the coronavirus."