Sporting director Lutz Pfannenstiel told the club website: "Peter has stepped up and lead the club on multiple occasions in recent years and gave his all when we needed him most.
"He has been a terrific servant and I have no doubts he will go on to be a manager in his own right.
"Whilst we are naturally disappointed to see Peter leave, changes to coaching staff are expected when a new head coach arrives and looks to make a fresh start."
Former Aberdeen assistant Tony Docherty, the former Dundee and Ross County manager who had returned to Pittodrie to help Leven until a permament appointment was made, also left last week.
Leven first became caretaker after the sacking of Barry Robson, taking charge of one game before reverting to first-team coach after Neil Warnock was appointed interim manager.
He also was caretaker while Aberdeen waited for the permanent appointment of Jimmy Thelin and stepped back in after the Swede exited this season.
In total, Leven was in charge for 24 games, winning nine and losing 10, eight of them in the current campaign.