The board adopted the measure by consensus in its morning session at Paris-based UNESCO. A draft form of the resolution had already been approved by a commission last week.
The resolution is not expected to have direct impact on Jerusalem itself, but it deepened tensions within UNESCO, which is also facing a diplomatic dispute between Japan and China that threatens funding.
The resolution, titled "Occupied Palestine," is the latest of several measures at the United Nations Educational, Scientific and Cultural Organisation over decades that Israelis see as evidence of ingrained anti-Israel bias within the United Nations, where Israel and its allies are far outnumbered by Arab countries and their supporters.
Israel last week suspended its ties with UNESCO over the draft resolution, which uses only the Islamic name for a hilltop compound sacred to both Jews and Muslims. The site includes the Western Wall, a remnant of the biblical temple and the holiest site where Jews can pray.
Jews refer to the hilltop compound in Jerusalem's Old City as the Temple Mount. Muslims refer to it as al-Haram al-Sharif, Arabic for the Noble Sanctuary, and it includes the Al-Aqsa mosque and the golden Dome of the Rock.
Israel had already suspended its funding to UNESCO when Palestinian membership was approved, along with the United States, which used to provide 22 percent of the agency's budget.
The longstanding dispute is also linked to Israel's refusal to grant visas to UNESCO experts to go in the country and assess the level of preservation of the holy sites in Jerusalem.
And now Japan, UNESCO's second-biggest funder, is threatening to halt funding. Japan announced last week it has withheld its annual UNESCO dues, saying it wants to make sure the UN body properly functions to foster trust among member nations.
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