Abbas claimed what he called a UN 'birth certificate' for a Palestinian state and got the backing of 138 countries in the 193 member assembly. Nine voted against and 41 abstained.
A Palestinian flag was unfurled in the General Assembly as the victory was pronounced. But Israeli Prime Minister Benjamin Netanyahu condemned what he called a 'venomous' speech by the Palestinian leader.
The vote lifts the Palestinian Authority from an observer entity to a 'non-member observer state' on a par with the Vatican.
Palestine has no vote on the General Assembly but is able to join UN agencies and potentially the International Criminal Court (ICC), where it could ask for an investigation of Israeli actions.
Palestinian President Mahmoud Abbas addresses the UN General Assembly before a vote on Palestinian non-member observer status in New York City. AFP
The Palestinian leadership says it wants to use the vote as a launchpad for renewed direct talks with Israel, which have been frozen for more than two years.
Abbas told the assembly the resolution was "the last chance to save the two-state solution."
In a 22-minute speech laced with references to Israel's operation against Gaza this month, Abbas said time for an accord is running out. "The rope of patience is shortening and hope is withering."
Afterwards, he said the vote had been 'historic'.
"Tomorrow we begin the real war," Abbas said at a celebration reception. "We have a long road and difficult road ahead of us. I don't want to spoil our victory tonight but the road ahead is still difficult."
The United States and Israel immediately condemned the vote, which US Secretary of State Hillary Clinton called 'counterproductive.'
US ambassador Susan Rice sternly told the General Assembly that the resolution would be 'an obstacle to peace' because it would not lead to a return to direct talks between the Israelis and Palestinians. Palestinian UN vote sets 'obstacles' to peace: US
"Today's grand pronouncements will soon fade. And the Palestinian people will wake up tomorrow and find that little about their lives has changed, save that the prospects of a durable peace have only receded," she said.
Palestinians wave posters of former leader Yasser Arafat and President Mahmoud Abbas as they watch the UN vote to upgrade the Palestine status. AP
The United States blocked a Palestinian application for full UN membership -- made by Abbas in September 2011 -- at the UN Security Council.
Netanyahu slammed Abbas. "The world watched a defamatory and venomous speech that was full of mendacious propaganda," his office said.
Israeli UN ambassador Ron Prosor said recognizing Palestine "will place further obstacles and preconditions to negotiations and peace" and could even lead to increased violence.
UN vote is 'victory' for Palestinians: Hamas
Abbas was warned earlier by UN leader Ban Ki-moon that the Middle East peace process is on "life support" and that both Netanyahu and Abbas must take action to revive talks.
The Palestinian leader did not make any reference to the possibility of joining the International Criminal Court -- a major worry for Israel which fears a possible investigation.
But Abbas said: "We will act responsibly and positively in our next steps, and we will to work to strengthen cooperation with the countries and peoples of the world for the sake of a just peace."
The vote could give a boost to Abbas who faces a mounting challenge from Hamas after the Israeli offensive on Gaza, diplomats said. The next stop for Palestinians: global courts
But Britain and Germany, which abstained, believe the Palestinians should have waited until after US President Barack Obama installed his new administration and Israel held elections before making its UN bid.
France voted for the resolution. "The Palestinian step comes at a difficult moment and there could be heavy repercussions," said French ambassador Gerard Araud.
France called on both sides to respond through the resumption of talks "and not through reprisals which will only play the game of the extremists," he added.
The Palestinians still face an uncertain future on the diplomatic stage. Despite their greater access to the UN system, there are divided opinions over whether they will be able to automatically join the ICC.
Palestinian envoys have said Abbas will not rush to join the court but could use it as leverage if Israel does not change its policies on settlements and other matters.
US, Israel isolated in condemning Palestine vote
The Palestinian Authority and UN agencies that accept Palestinian participation could also lose hundreds of millions of dollars in financing because of the vote.
Washington has warned Abbas he risks losing around $200 million in aid, which is blocked in the US Congress.
(With inputs from AP and Reuters)