Under the Reagan Administration, the U.S. quit UNESCO in 1984, at the time accusing the agency of a pro- Soviet Union bias.
Washington's withdrawal is set to take effect on December 21, 2018, when it will establish an "observer mission" to replace its representation at the agency.
The UN General Assembly President Miroslav Lajčák is also "concerned that the decision by the United States to withdraw could have adverse impacts upon the important work of UNESCO", according to a statement from his spokesperson.
Unesco is best known for its World Heritage programme to protect cultural sites and traditions around the world.
The United States announced on Thursday that it is pulling out of UNESCO because of what the Trump administration sees as its anti-Israel bias and a need for "fundamental reform".
The U.S. stopped funding UNESCO after it voted to include Palestine as a member state in 2011, but the State Department has maintained a UNESCO office and sought to weigh in on policy behind the scenes.
"The objective of UNESCO is a good one", US Ambassador to the United Nations Nikki Haley said in a statement. Unesco was dependent on the United States for 22 percent of its budget, then about $70 million a year.
"At the time when conflicts continue to tear apart societies across the world, it is deeply regrettable for the United States to withdraw from the United Nations agency promoting education for peace and protecting culture under attack", Bokova said.
USA officials said Secretary of State Rex Tillerson made the decision and it was not discussed with other countries.
The organization has a long history of taking anti-Israel measures, and supporting resolutions against the Jewish state.
The Trump administration has been preparing for a likely withdrawal for months, and a decision was expected before the end of the year, according to USA officials.
The third round saw the breakthrough of French candidate Audrey Azouley, who secured 18 out of 58 votes of the UNESCO Executive Board, sharing top spot with Qatari candidate Hammad bin Al-Kawari.
A Downing Street spokesman said: "The Government is committed to continued United Kingdom membership of Unesco and to working with other member states in support of its important work". It extended membership to Palestine in 2011. "The organisation's absurd and shameful resolutions against Israel have consequences".
The decision follows a string of UNESCO decisions that have drawn criticism from the U.S. and Israel.
Israeli Prime Minister Benjamin Netanyahu called the vote "another delusional decision" by UNESCO, which promotes education, cultural development and free media initiatives around the world.
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