The former Hungary midfielder, who also works as a coach for Hertha Berlin's youth set-up, was appointed on an interim basis after Attila Pinter's dismissal in September.
"Besides his job at the national team, Dardai remains with Hertha Berlin, who were absolutely correct during the negotiations and agreed on the terms of the manager's future work timetable,” the HFA's vice president Sandor Berzi said at a news conference.
Dardai's popularity is growing each day and under his guidance Hungary have taken seven points from their last three Euro 2016 qualifiers, drawing 1-1 in Romania and beating both the Faroe Islands and Finland 1-0.
"It was a tough decision, I had to talk it over with Hertha, with the HFA and with my family and when my eight-year-old son, Bence, told me to keep working with the national team, I decided to give it a go," Dardai said in a TV interview.
"With feeling all the support from the Hungarian people, media and players I could not jump out of it, I have to carry on."
Hungary are currently third in Group F, behind Romania and Northern Ireland.
(Reporting by Zoltan Fazekas; editing by Toby Davis)
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