UNESCO is a specialized agency in the United Nations that encourages global peace and security through education, science, culture and communication.
A press statement from the State Department says the decision was also based on "the need for fundamental reform in the organization" as well as stacking up bills the US owes UNESCO.
The withdrawal, effective December 31, 2018, won't be the first for the United States.
She paid tribute to what she said had been a meaningful relationship between UNESCO and the U.S., saying: "since 2011, we have deepened the partnership between the United States and UNESCO, which has never been so meaningful".
UNESCO, which is best known for producing the list of World Heritage sites that includes the Grand Canyon and other USA attractions, has been the scene of diplomatic flare-ups in recent years after Arab countries succeeded in passing a number of resolutions critical of Israel. Israel has accused UNESCO of making a politically motivated move, part of what it says is an attempt to deny the Jewish character and heritage of certain key sites in the Holy Land.
Unesco said the withdrawal was a loss to the "UN family" and to multilateralism.
Bokova released a statement in light of the news.
"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", the statement said.
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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 department also voiced concerns about an anti-Israel bias at UNESCO.
That year the U.S. stopped paying into UNESCO but did not officially withdraw.
The US was angered in 2011 when UNESCO members granted Palestine full membership of the body, despite opposition from its ally Israel.
US officials said Secretary of State Rex Tillerson made the decision and it was not discussed with other countries. After he was elected but before he became president, Mr. Trump made an extraordinary intervention on the world stage by criticizing the Obama administration's decision not to block a United Nations resolution criticizing Israeli settlements.
The 2016 resolution condemned Israel's "escalating aggressions" regarding a holy site in Jerusalem's Old City, known to Muslims as al-Haram al-Sharif and to Jews as the Temple Mount.
In addition, the Trump administration's proposed budget for the next fiscal year contains no provision for the possibility that Unesco funding restrictions might be lifted.
UNESCO also works to improve education for girls in poor countries, help them enter scientific fields, defend media freedom and coordinate world knowledge about climate change, among other activities.