Leekens, 68, takes charge after Hungary parted ways this month with German Bernd Stock, following the unsuccessful qualifying campaign for next year's World Cup in Russia.
Hungary finished as runners-up in the 1938 and 1954 World Cups but have not qualified for the global showpiece tournament since 1986.
Leekens, who has signed a two-year-contract, has had two spells as manager of his native Belgium.
The first included a run to the 1998 World Cup in France, and between 2010-2012 he laid the foundations for the team that reached the quarter-finals of the 2014 tournament and last year's European Championship.
He has also coached Tunisia and Algeria.
"I cannot guarantee success, only hard work," Leekens told a news conference on Monday. "I will put together a team that will fight till the end to get to the next European Championship through the qualifiers."
Former defender Zoltan Szelesi will remain as interim coach for the remaining fixtures this year, friendlies against Luxembourg on Nov. 10 and Costa Rica four days later.
(Reporting by Zoltan Fazekas,; Editing by Christian Radnedge)
