The report calls on both Israel and the Palestinians to investigate within three months accusations of human-rights violations during the 22-day conflict in December and January.
Most of the criticism in the Goldstone report was directed towards Israel's conduct during the offensive, in which human rights organisations say about 1,400 Palestinians - many of them women and children - were killed.
Thirteen Israelis, including three civilians, were killed over the course of the war.
The report concluded that Israel used disproportionate force in the war, deliberately targeting Gaza civilians, using them as human shields, and destroying civilian infrastructure.
Ali Treki, the General Assembly president, called the vote "an important declaration against impunity. It is a call for justice and accountability".
"Without justice, there can be no progress towards peace. A human being should be treated as a human being, regardless of his or her religion, race or nationality," he said.
Apart from Israel and the US, a number of European countries including Italy, the Netherlands, Poland and the Czech Republic, voted against the resolution.
The Netherlands' representative said, however, he supported elements in the text, which sought to pursue inquiries into violations of human rights and international law.
Britain and France were among EU member nations who abstained. Most developing countries voted in favour of endorsing the report.
Jorge Valero, Venezuela's ambassador to the UN, endorsing the report, said Israel should be brought to justice for crimes against Palestinians, and those responsible for the "operation of terror".
Nassir Abdulaziz al-Nasser, Qatar's ambassador to the UN, said the Goldstone report pointed to crimes committed by the Israel that amounted to war crimes and crimes against humanity, including murder, torture and serious physical and psychological harm to civilians.
Riyad Mansour, the Palestinian UN observer called it "an important night in the history of the General Assembly and the history of fighting against impunity and seeking accountability".
'Disproportionate and systematic'
Earlier, speaking ahead of the final UN vote, Mansour said the Goldstone report had concluded that the Israeli military onslaught "was planned in all of its phases as a deliberately disproportionate and systematic attack aimed at punishing, humiliating and terrorising the Palestinian civilian population".
But Daniel Carmon, Israel's deputy ambassador to the UN, told the assembly that the resolution "endorses and legitimises a deeply flawed, one-sided and prejudiced report of the discredited Human Rights Council and its politicised work that bends both fact and law".
Alejandro Wolff, the US deputy ambasssador to the UN, also accused the the resolution of being flawed, saying that it failed to name Hamas, the Palestinian group that has de facto control of Gaza.
The non-binding resolution passed on Thursday by the General Assembly asks Ban Ki-moon, the UN secretary-general, to pass the report to the UN Security Council.
However, diplomats have said that the five permanent members of the 15-member Security Council have signalled that they are opposed to council involvement - meaning that it is unlikely that the 15-nation body would take action.
The debate at the General Assembly was called for by the Arab UN group, with the backing of the 118-member Non-Aligned Movement (NAM).