The announcement comes a day after taxi drivers staged violent protests against Uber in France, where the service has been illegal since January, but continues to operate as the law has proved difficult to enforce.
Cabbies across Europe are furious at what they see as unfair competition from Uber, which puts customers in touch with private drivers at prices lower than those of traditional taxis.
In Budapest, several hundred drivers took to the streets last week demanding that the government regulate Uber the same way as their own services.
In response, Hungary's government has now approved a new decree laying out technical requirements for cars and licensing rules for drivers providing "personal transport services".
Importantly, the rules will also apply to rides ordered through mobile phones and require drivers who use Uber to be licenced taxi drivers.
The decree did not mean Uber would be banned, but rather aimed to regulate who could provide taxi services, said Janos Fonagy, the state secretary in charge of the case.
"The government does not want to stand in the way of innovative solutions," he told a press conference.
If licenced taxi drivers want to use Uber's application to get fares, they may, Fonagy said.
The new rules, due to come into effect in 2018, will also oblige taxi drivers to take a refresher course and pass an exam on road rules every five years.
Since Uber entered the Hungarian market in 2014, taxi orders have been dropping sharply in the country.
The US company has become one of the world's most valuable startups, worth an estimated $50 billion, as it has expanded to more than 50 countries.
But it has faced regulatory hurdles and protests from established taxi operators in most locations where it has launched.