Earlier this month, Hosszu and her team mates demanded a complete overhaul of the country's Swimming Association in a bitter dispute that has threatened to damage Budapest's bid to host the 2024 Summer Olympics.
"I hereby resign because I feel this is the best way for me to help now," Gyarfas said in a statement to state news agency MTI.
"I became chairman of the Swimming Association in 1993... It was great to be a part of the five European Championships Hungary hosted and I am happy to have been there when we won the right to host the World Championships."
Hosszu accused Gyarfas of running Hungarian swimming in an authoritarian and opaque manner, accusations he strongly denies.
As well as his domestic role, Gyarfas is also an influential vice president of the sport's global governing body FINA, who will organise the World Aquatics Championships in Hungary next year.
It was not immediately clear who would succeed Gyarfas or how his resignation would affect his position with FINA.
(Editing by John O'Brien)
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