Keane took charge of Ferencvaros in January and led them to the Hungarian title. This season, Ferencvaros are unbeaten in the Europa League.
The new deal is for an undisclosed length.
"I'm happy to continue this journey," said Keane, who was raised as a potential replacement for Thomas Frank at former club Tottenham last week.
"I'm really enjoying it. It's a good place to be. Amazing supporters, good relationships with everybody at the club. The president has been fantastic and can see the vision I have for the club. And stability is very important. I'm very happy to sign and stay."
Ferencvaros president Gabor Kubatov said: "Robbie feels very comfortable in Budapest. He loves the people, the Hungarian restaurants, the food. It is as though he likes this fabric and has embroidered himself into it.
"The fans love him too. He is a winner. Relentless and very motivated."