The United States - one of the body's founding members - has withdrawn once before under president Ronald Reagan, who quit in 1984 over alleged financial mismanagement and anti-US bias in some of its policies.
Netanyahu accused UNESCO of "becoming a Theater of Absurd because instead of preserving history, it twists it".
Washington said it would establish an "observer mission" to replace its representation at the agency.
Israel has also announced today that they will be quitting the United Nations agency, and Israeli Prime Minister Benjamin Netanyahu called the decision by the USA "brave and moral".
"UNESCO is about promoting our ideals and values through culture, education and science", France's United Nations ambassador Francois Delattre told reporters in NY, adding that "we need an America that stays committed to world affairs".
Washington intends to participate in the fulfillment by UNESCO of a number of its functions, including the protection of the world cultural heritage, the protection of press freedom, the promotion of scientific cooperation and the educational process.More news: Apple's Face ID may not be iPhone X exclusive for long
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.
"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", she said in an extensive statement Thursday.
In recent years, Israel has repeatedly complained about what it says is the body taking sides in disputes over cultural heritage sites in Jerusalem and the Palestinian territories.
"It's a loss to UNESCO, it's a loss to the family of the United Nations and it's a loss to multilateralism", Bokova said in a statement.
"This is another example of the Trump's administration's profound ambivalence and concern about the way the U.N.is structured and behaves, and it shows the administration's determination to separate itself from its predecessors", said Aaron David Miller, a former Middle East negotiator and adviser in Republican and Democratic administrations.
The United Nation's education, cultural and scientific agency has passed several resolutions against Israel.
The U.S. joined UNESCO at its creation in 1945.
Hegadorn said the USA would remain a force at the cultural agency in the same way as it was from 1984, when the country withdrew under then-President Ronald Reagan.