Gary McSheffrey had been the manager of Doncaster Rovers.
McSheffrey was in charge of the club last season when they were demoted from the top flight.
The results in League Two were "largely positive" but they cited a lack of progress as the reason for their decision.
Gribble and Green have been put in charge.
"While results so far in League Two have been largely positive, there has been a growing concern over the standard of performances in matches and a lack of progress between games," the club said in a statement.
This is making it hard for us to achieve our goals.
McSheffrey had been Doncaster's under-18s manager when he was appointed as first-team boss last December, initially on an interim basis and then permanently.
Even if they only went down on the final day of last season as they were 22nd in League One, they didn't climb out of the bottom half of the league.
After making a number of new signings in the summer, Doncaster started their League Two campaign well and were third after a win at Northampton Town.
They have just two wins from eight games since that time.
After winning 14 of his 46 games in charge, the club's board felt it was in their best interests to get rid of McSheffrey.
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