The former Hungary midfielder was appointed on an interim basis following Attila Pinter's dismissal in September and had intended to remain in the role until the end of their Euro 2016 qualifying campaign.
Having been named Hertha manager in May it was decided Dardai would relinquish his Hungary duties with Stock taking the reigns for the remaining four qualifying fixtures.
"I accept and totally respect Hertha Berlin's decision," Dardai, 39, told Hertha's official website (www.herthabsc.de).
"We would want a smooth season with the club and it takes all from me, all of my energy. I have a Hungarian heart, I love my country, and I think I helped the team move forward during my reign.
"I feel proud to have had the chance to be national coach. I believe the team can fulfil the expectations and reach the European Championship."
Hungary are third, behind Romania and Northern Ireland, in Group F on 11 points and face Romania in Budapest in September.
Storck, 52, was appointed sports director in February before becoming head coach of the Hungarian Under-20 team for the World Cup in New Zealand in June where they lost to eventual winners Serbia.
(Reporting by Zoltan Fazekas, editing by Tom Hayward)
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