Wilmots has been given a two-year contract, the Belgian football association (FA) said in a statement on Wednesday.
"Marc Wilmots took on full responsibility for the team a month ago in unexpected and difficult circumstances and since then confirmed his excellent work of the previous years at all levels," the Belgian FA said in a statement.
The former Belgium international, who won 70 caps, had been Leekens' assistant and took over as caretaker coach for the team's recent 2-2 draw with Montenegro and 1-0 loss to England.
Wilmots' task will be to qualify Belgium for a major tournament for the first time since the 2002 World Cup.
"I said 'no' to the option. My first challenge is (the World Cup in) Brazil. That's tough enough. We'll see how things evolve after that," he said in a video posted on the website.
Wilmots was an attacking midfielder dubbed "Kampfschwein" (fighting pig) by adoring fans at German club Schalke 04, where he won the UEFA Cup in 1997 after scoring the winning penalty in a shootout.
