The reformed human rights body is designed to be more effective and to replace the current, Geneva-based UN Human Rights Commission.
The current commission has seen its credibility tarnished by the presence among its 53 members of notorious human rights abusers such as China, Cuba, Sudan and Zimbabwe.
The vote was 170 countries in favor and four against, the United States, Israel, Palau and Marshall Islands, and three abstentions being Iran, Venezuela and Belarus.
The Assembly vote had been delayed for several weeks to try to bring the United States on board.
But in explaining his no vote, US Ambassador John Bolton said: "We did not have sufficient confidence in this text to able to say the Human Rights Council will be better than its predecessor."
"That said, the United States will work cooperatively with other member states to make the council as strong and effective as it can be," he added.
Speaking before the vote, Cuban ambassador Rodrigo Malmierca said despite reservations, his country would back the resolution but launched a scathing attack on the United States.
"Will it be possible in the new Council to approve a resolution demanding that the United States be held accountable for the tortures and other serious human rights violations perpetrated" at its Guantanamo Bay, Cuba prison camp, at the Abu Ghraib prison and "at secret detention centers operated by the CIA in Europe?," he added.
Venezuelan ambassador Fermin Toro for his part said his country would abstain because of "serious doubts" about elements of the text.
The resolution, the culmination of of five months of negotiations, calls for a council of 47 members that would be elected by absolute majority of the General Assembly. The panel would meet three times a year for a minimum of 10 weeks.
The US wanted a smaller body whose members would be elected by a two-thirds majority.