United States has earlier pulled out from UNESCO as well.
Unesco, the United Nations Educational, Scientific and Cultural Organization known for its designation of world heritage sites, is a global development agency with missions that include promoting sex education, literacy, clean water and equality for women.
Bokova's two terms as director have been deeply scarred by the 2011 UNESCO vote to include Palestine as a member, funding troubles and repeated resolutions seen as anti-Israel.
It says the withdrawal will take effect December 31, 2018.
The United States notified UNESCO, a UN cultural organization, of its withdrawal, the U.S. State announced on October 12.
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A representative of the US delegation to UNESCO referred Reuters to the State Department.
It is not the first time the US has withdrawn.
The magazine said the decision was aimed at saving money and to protest what the U.S believes is UNESCO's anti-Israel stance.
"This decision was not taken lightly, and reflects USA concerns with mounting arrears at Unesco, the need for fundamental reform in the organization, and continuing anti-Israel bias at Unesco", the department said, adding that the United States would seek to "remain engaged ... as a non-member observer state in order to contribute U.S. views, perspectives and expertise".
USA officials have told The Associated Press that the United States is pulling out of UNESCO, after repeated criticism of resolutions by the U.N. cultural agency that Washington sees as anti-Israel.