The legislation is branded as "Stop Soros" and the Hungarian government warned on Monday that legislative measures may yet become tighter.
"Faced with an increasingly repressive political and legal environment in Hungary, the Open Society Foundations are moving their Budapest-based global operations and staff to the German capital, Berlin", the group said in a statement.
The European Union said this month it aims to cut funds to member states that undermine judicial independence, a move that could cost Hungary and Poland millions of euros.
Patrick Gaspard, president of the Open Society Foundations, said on Tuesday that Budapest had "denigrated and misrepresented" the organization's work and repressed civil society "for the sake of political gain". Warsaw faces possible moves to suspend its membership rights.
Orban's Fidesz also ran an anti-immigrant billboard campaign, underwritten by the Hungarian government, which showed a picture of Soros laughing alongside the words, "Let's not leave Soros the last laugh".
A loose-knit group of George Soros-financed foundations is leaving Hungary as the government's nationalist leader continues cracking down on the billionaire's influence in the country.
Scientists successfully transfer memory from one snail to another
Extracting RNA from these trained animals and injecting it into untrained animals resulted in a similar sensitized response. The long-term memories are considered to be stored at the synapses of the brain or the junctions between the nerve cells.
The pro-democracy group said it was pulling out a day after the right-wing government of Prime Minister Viktor Orban announced it would tighten restrictions on non-governmental organizations, under a law dubbed the "Stop Soros " bill.
It would allow the interior minister to ban any NGOs active in the immigration field deemed to pose a "national security risk".
The OSF is a top donor of the Hungarian Helsinki Committee, which campaigns for human rights.
Another Soros institution funded by Soros, Budapest's Central European University, may also be forced to shutter operations in Hungary.
The CEU - which plans to open a satellite campus in Vienna - has agreed a deal with a USA college to meet new conditions imposed by Hungary, but the government is yet to approve the agreement. Its rector, Michael Ignatieff, said new students in 2019 might have to enrol across the border in Austria if the CEU fails to strike a deal with Hungary under the new law, which sparked street protests and an European Union legal challenge.
"CEU can not go into another academic year in a situation of legal uncertainty", its rector Michael Ignatieff said on Tuesday.