Leekens, who has signed a three-season contract, will cease his involvement with the national side immediately.
The 62-year-old was to have announced his squad on Tuesday to face Montenegro and England in friendlies in the coming weeks and to lead Belgium in World Cup 2014 qualifiers starting with Wales in September.
Belgian football association chairman Francois De Keersmaecker described Leekens' sudden departure as "beneath contempt", saying he had only learned the news early on Sunday afternoon.
"I am enormously disappointed and outraged... This is the biggest shock of my career. This beats everything," he told Belgian radio.
Leekens told a news conference at Club Bruges on Sunday evening that he had also been surprised by events.
"I understand that the FA is deeply disappointed, but I feel that my work with the national side was 90 per cent done," he said.
"The only thing missing is the finishing touch, qualification for the World Cup 2014, but I am convinced that my players will complete this task."
Belgium have failed to qualify for a major tournament since the 2002 World Cup, although there is increasing talk of a current 'golden generation' with the likes of Vincent Kompany, captain of newly crowned English champions Manchester City, Everton playmaker Marouane Fellaini, and Jan Vertonghen and Kevin Mirallas, named footballers of the year in the Netherlands and Greece respectively.
The Belgian football association said it would meet on Monday to discuss a possible successor.
Ariel Jacobs, coach of new champions Anderlecht, and Jose Riga, in charge at Standard Liege, also announced they were quitting after Sunday's final round of matches.
Leekens will succeed German Christoph Daum, who announced his intention to leave last week after steering Bruges to second place in the Belgian championship.
He had been national manager, for a second time, since 2010, when he stepped in following Dutchman Dick Advocaat's abrupt departure after just six months to coach Russia.
Leekens played as a central defender for Club Bruges between 1971 and 1982 and coached the side from 1989-91. He won the championship in his first season managing the club.