The International Day of Commemoration will be held every year on Jan. 27.
Israel's U.N. Ambassador Dan Gillerman thanked the 191 members of the General Assembly "at this unique and historic moment ... for adopting this unprecedented resolution."
Secretary-General Kofi Annan said the annual commemoration will serve as "an important reminder of the universal lessons of the Holocaust, a unique evil which cannot simply be consigned to the past and forgotten," U.N. spokesman Stephane Dujarric said.
There was no vote on the resolution. Instead, General Assembly President Jan Eliasson banged the gavel signifying consensus after asking whether there were any objections and hearing none.
But after the vote, Egypt's U.N. Ambassador Maged Abdelaziz complained that the day should commemorate all victims of genocide - "without discrimination on the basis of religious or ethnic background" - and not be limited just to victims of the Holocaust.
"We believe that no one should have the monopoly of suffering," he said.
Venezuela's Ambassador Imeria Nunez de Odreman also expressed concern that it did not encompass other recent genocides including those in Cambodia, Rwanda and Kosovo.
She also pointed to the atomic bombs dropped on Hiroshima and Nagasaki in World War II as examples of "devastating destruction" that occurred "with no justification" and should be included in the resolution's stance against human atrocities.
But Jordan's U.N. Ambassador Prince Zeid al Hussein supported the resolution, saying people must "draw on our memories" of the Holocaust to prevent future genocide and "other expressions" of hatred in the 21st century.
"Ultimately, we hope this occasion and ones like this will enable us to derive the right lessons from the atrocities committed by the Nazis and by their accomplices, to ensure such crimes will not come to blight," he said.
The resolution emphasizes both "the duty to remember" and "the duty to educate" future generations about the mass slaughter ordered out by Adolf Hitler, Germany's wartime Nazi leader.
It rejects any denial of the Holocaust, condemns discrimination and violence based on religion or ethnicity, and calls for the U.N. to establish an outreach program to encourage the public to engage in Holocaust remembrance activities.
Annan looks forward to establishing programs "to mobilize civil society for Holocaust remembrance and education, in order to help prevent future acts of genocide," Dujarric said.
The resolution, which Gillerman introduced Monday, was sponsored initially by Israel, the United States, Australia, Canada and Russia. Gillerman said after Tuesday's vote that it had 104 co-sponsors.
The United Nations was established from the ashes of World War II, and as the world marks the 60th anniversaries of both the U.N.'s founding and the end of the war, Gillerman and Eliasson said the Nazi slaughter must never be forgotten.
"The U.N. bears a special responsibility to ensure that the Holocaust and its lessons are never forgotten and that this tragedy will forever stand as a warning to all people of the dangers of hatred, bigotry, racism and prejudice," said Gillerman.
Eliasson recalled that part of the U.N.'s original mission was to make sure such an "unspeakable atrocity" as the Holocaust never occurred again.
Eliasson and other speakers noted, however, that the Holocaust and World War II did not mark the end of crimes of genocide.
"The Holocaust also reminds us of the genocide crimes committed since World War II," he said. "It must therefor be a unifying historic warning around which we must rally. We cannot continue to repeat saying `never again.'"