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France's National Front leader Marine Le Pen tweeted "Victory for freedom" and said the French must now also have the right to choose.
Dutch anti-immigration politician, Geert Wilders, said the Netherlands now deserved a "Nexit" vote.
The UK on Thursday voted by 52% to 48% to leave the European Union after 43 years, in a historic referendum.
Analysts say EU politicians will fear a domino effect that could threaten the whole organisation.
Ms Le Pen hailed the UK vote, tweeting: "Victory for freedom. As I've been saying for years, we must now have the same referendum in France and other EU countries."
She is the front-runner among candidates for the presidential election in 2017 but opinion polls suggest she would lose a run-off vote.
Last Friday, Ms Le Pen had told a gathering of far-right parties in Vienna: "France has possibly 1,000 more reasons to want to leave the EU than the English."
She said the EU was responsible for high unemployment and failing to keep out "smugglers, terrorists and economic migrants".
Mr Wilders, leader of the Party for Freedom in the Netherlands, said in a statement: "We want to be in charge of our own country, our own money, our own borders, and our own immigration policy.
"As quickly as possible the Dutch need to get the opportunity to have their say about Dutch membership of the European Union."
The Netherlands faces a general election in March and some opinion polls suggest Mr Wilders is leading.
He said: "If I become prime minister, there will be a referendum in the Netherlands on leaving the European Union. Let the Dutch people decide."
A recent Dutch survey suggested 54% of the people in the Netherlands want a referendum.
Austrian Foreign Minister Sebastian Kurz said he believed the EU would survive the UK exit, but that "a domino effect on other countries couldn't be ruled out".
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