These passengers are allowed to enter:

• citizens of Hungary and their family members;
• passengers with a residence permit issued by Hungary with a validity longer than 90 days;
• holders of a “D” visa issued by Hungary;
• passengers transiting Hungary to another country. They must prove that they are allowed to enter the final destination or a neighboring country in order to reach their final destination;
• passengers traveling on business;
• holders of a signed and stamped letter issued by the Deputy-Chief Officer of the National Police;
• holders of a positive COVID-19 test result of a test taken not more than 6 months before arrival. They must also have a recovery certificate;
• holders of an immunity COVID-19 certificate issued by Albania, Bahrain, Croatia, Cyprus, Czechia, Georgia, Hungary, Kazakhstan, Moldova (Rep.), Mongolia, Montenegro, Morocco, North Macedonia (Rep.), Romania, the Russian Federation, San Marino, Serbia, Slovakia, Slovenia, Switzerland, Turkey, Ukraine or Uzbekistan. Minors under 18 years are allowed to travel with them;
• holders of a negative COVID-19 PCR test result in English or Hungarian issued not more than 72 hours before arrival. The test result must be issued in Albania, Australia, Austria, Azerbaijan, Bahrain, Belgium, Bulgaria, Canada, Chile, China, Croatia, Cyprus, Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland (Rep.), Israel, Italy, Japan, Kazakhstan, Korea (Rep.), Kyrgyzstan, Latvia, Lithuania, Luxembourg, Malta, Mexico, Montenegro, Netherlands, New Zealand, North Macedonia (Rep.), Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, the Russian Federation, Turkey, the United Arab Emirates, the United Kingdom, the USA or Uzbekistan;
• holders of an EU Digital Covid Certificate (EU DCC) showing that they:
• have received at least one dose of the vaccine at most 1 year before arrival. Vaccines accepted are: AstraZeneca (Vaxzevria), Janssen, Moderna, Pfizer-BioNTech, Sinopharm and Sputnik V; or
• have a positive COVID-19 test taken at most 6 months before arrival and a recovery certificate; or
• have a negative COVID-19 PCR test result issued at most 72 hours before arrival.

More details can be found here

Arriving passengers could be subject to medical screening and quarantine for 10 days.