The motion was passed by a substantial majority, despite strong opposition from the United States and Israel.
A US state department spokeswoman said a payment of some $60m (£37m) due next month would not be made.
Membership dues paid by the US account for about a fifth of the organisation's annual budget.
This is the first UN agency the Palestinians have sought to join since submitting their bid for recognition to the Security Council in September.
The UN Security Council will vote next month on whether to grant the Palestinians full UN membership.
Widespread applause greeted the result of Monday's vote in the chamber - of 173 countries taking part, 107 were in favour, 14 voted against and 52 abstained.
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Analysis
Jon Donnison
BBC News, Ramallah
This is a historic day, said Palestinian deputy Minister of Antiquities Hamdan Taha, beaming from ear to ear in Ramallah.
Unesco membership may seem a strange and short step to Palestinian statehood. But leaders here see it as part of a broader push to get international recognition and pressure Israel. They see it as a warm-up for a more important vote next month when the UN Security Council will decide whether to admit Palestine as a full member state.
The US has veto power at the security council and has threatened to use it. It had no such power at Unesco so instead lobbied hard to try and force the Palestinians to back down. It will likely cut all US funding for Unesco - $70m a year, or 22% of its annual budget.
But Unesco members seemed to put politics before money, clearly voting in favour of the Palestinian bid. This was a failure of US power, one Palestinian official told me.
The victory will give a boost to the Palestinian President Mahmoud Abbas. He lost ground to his rival Hamas when the Islamist movement secured the release of hundreds of Palestinian prisoners in exchange for captured Israeli soldier Gilad Shalit two weeks ago.
Arab states were instrumental in getting the vote passed despite intense opposition from the US.
In an emotional session, China, Russia, India, Brazil and South Africa voted in favour of Palestinian membership, while the US, Canada and Germany voted against and the UK abstained.
Membership of Unesco - perhaps best known for its World Heritage Sites - is seen by Palestinian leaders as part of a broader push to get international recognition and put pressure on Israel.
"This vote will erase a tiny part of the injustice done to the Palestinian people," Palestinian Foreign Minister Riyad al-Malki told the meeting of the UN educational, scientific and cultural organisation in Paris, after the result was announced.
One of the first moves Palestinians are set to make is to apply for world heritage status for sites on occupied Palestinian land such as the Church of the Nativity in Bethlehem, the Associated Press news agency reports.
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