The legislation is branded as "Stop Soros" and the Hungarian government warned on Monday that legislative measures may yet become tighter.
Soros was a particular target of vitriol, with "Stop Soros" billboards being displayed around the country as a law was proposed that would curb NGOs that posed a "national security risk".
"Faced with an increasingly repressive political and legal environment in Hungary, the Open Society Foundations are moving their Budapest-based worldwide operations and staff to the German capital, Berlin", the group said in a statement.
Soros' Open Society Foundations, which promote democracy and free speech, have also endured threats of legal sanctions from the government. In addition, the new law bans NGO activity geared towards migrant human rights advocacy.
When news of the Open Society Foundations' possible departure from Hungary broke in April, Orban said: "You might understand if I don't cry my eyes out".
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The OSF said it would "pursue all available legal avenues to defend the fundamental rights that are threatened by the legislation" and "continue to support the important work of civil society groups in Hungary". Pro-government media recently began publishing false accusations about individual academics, civil society members, and Foundations staff.
The building that houses the Budapest offices of the Open Society Foundations in Budapest, Hungary.
"CEU can not go into another academic year in a situation of legal uncertainty", its rector Michael Ignatieff said on Tuesday.
The Open Society Foundations have a long legacy in Hungary, where Soros was born and where he began his philanthropy in Europe. Within its first decade, Open Society funded milk for schoolchildren, brought equipment to hospitals, and helped the country's poorest and most vulnerable.
Orban is leveraging his recent massive electoral victory to restrict the political influence of NGOs, many of which received millions from Soros, a Hungarian who escaped the country before Nazis invaded.