Leekens left the post on Sunday after signing a three-year deal to become the new manager of Club Brugge.
The 43-year-old Wilmots, an assistant under Leekens, will take charge of the side for their upcoming friendlies against Montenegro and England before a new full-time coach is appointed.
Reports in the local media had tipped incumbent Morocco boss Eric Gerets to land the role, but the former Marseille gaffer told Flemish TV station VTM that he would honour his contract that runs until 2014.
Gerets said: "Before 2014, I cannot become coach of the Red Devils. I only once broke my contract, for private reasons, and I have a bitter memory.
"I don't want to go through that a second time. In my case, I will respect my contract with Morocco."