The resolution elevates their status from "non-member observer entity" to "non-member observer state," the same category as the Vatican, which Palestinians hope will provide new leverage in their dealings with Israel.
Its leaders had been working with dozens of supporting nations to develop a formal draft, enlisting the backing of European countries such as France and Spain.
The vote was 138 delegates in favor of the measure, nine against and 41 abstentions, including Germany.
Palestinian Authority President Mahmoud Abbas said the move, which many call symbolic, represents a "last chance to save the two-state solution."
It comes on the heels of an eight-day conflict that raged between Israel and Hamas fighters, where a series of airstrikes and rocket launches drew international attention and threatened regional stability.
"We did not come here seeking to delegitimize a state established years ago, and that is Israel; rather we came to affirm the legitimacy of the state that must now achieve its independence, and that is Palestine," he said.
But Israel's U.N. ambassador Ron Prosor said the move largely ignores the specifics of longstanding issues, such as settlements in disputed lands, and cannot substitute for direct negotiations between Jerusalem and Ramallah.
This resolution "doesn't pursue peace," Prosor said, criticizing Abbas for being unable to represent the Gaza Strip, where a Hamas-controlled government presides.
"It pushes it backwards," he said.
The effort stalled last year when it became apparent that the bid could not get the necessary support in the Security Council. Observer state status does not require Security Council approval, unlike full membership recognition.
The observer status resolution needs only a majority of the U.N.'s 193 members to approve.
The United States and Israel have remained steadfast in their opposition, saying the move will not advance the cause of Middle East peace.
U.S. Ambassador to the U.N. Susan Rice said American leaders could not support a measure that circumvents direct talks and cautioned that Thursday's decision did "not establish Palestine as a state."
Rice urged both sides to the resume direct negotiations without preconditions.
"Israel is prepared to live in peace with a Palestinian state," Israeli Prime Minister Benjamin Netanyahu said Thursday. "But for peace to endure, Israel's security must be protected, the Palestinians must recognize the Jewish state and they must be prepared to end the conflict with Israel once and for all."
Israeli government spokesman Mark Regev called the resolution "political theater."
But Palestinian leaders have said they had the right to go to the U.N. because Israel failed to comply with agreements signed more than two decades ago.