Grant, who steered Chelsea to the 2008 Champions League final before losing to Manchester United on penalties, declined to specify the reasons for his decision.
"I would like to keep the details to myself, I planned to stay longer but life is often unpredictable," the 57-year old Israeli told a news conference.
"I am sad to be leaving but such is life, we all have to look forward and that means the club, the fans and myself. I opted to activate the clause allowing me to leave before my contract expires," he said.
Grant took over in January from fans' favourite Aleksandar Stanojevic when Partizan were 10 points clear of traditional city rivals Red Star at the top of the first division.
He was quickly at loggerheads with Partizan's faithful after a pair of draws against modest opposition had slashed the advantage to six points and was pelted by lighters in his first home game in charge, a 0-0 draw with Sloboda Sevojno.
Losing three successive derbies to Red Star, two in the cup semi-final and the league fixture after Partizan had already secured the title with three games to spare, also did not help Grant's cause as he came under mounting pressure.
"I was brought up to look at the positive side of things and I will take great memories with me from Belgrade," said Grant.
"I can understand the fans were disappointed after the derby defeats but they stuck with us and that's how it works. Players and coaches come and go while the club is bigger than any one of us and lives on."
Former Partizan coach Vladimir Vermezovic, who steered the club to the 2005 league title, has been tipped as the prime candidate to take over from Grant after the champions entertain relegated Metalac in their last game of the season on Sunday.
Partizan won a record fifth successive league title under Grant and their 24th overall, meaning they are just one short of equalling Red Star's record.
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