President Mahmud Abbas will personally submit the request seeking to upgrade their rank from an observer entity to that of a non-member observer state before the UN General Assembly.
If the request is approved by the 193 member states of the UN General Assembly, it will give the Palestinians access to a range of UN agencies and also potentially to the International Criminal Court.
The move is strongly opposed by the United States and Israel, who say a Palestinian state should only emerge out of bilateral negotiations.
The latest bid comes 14 months after Abbas first approached the UN, seeking full state membership in a request which stalled at the Security Council after the United States threatened to use its veto.
But Thursday's resolution is likely to pass easily, requiring only a simple majority to go through.
"We are going to the United Nations fully confident in our steps. We will have our rights because you are with us," Abbas told a gathering of around a thousand people who rallied in Ramallah on Sunday.
"We ask for a just peace, which is agreed on by the international community which will give us our state with east Jerusalem as its capital. Without that, there is no hope at all," he said.
As Abbas took off from Amman for New York, France announced it would vote in favour of the resolution in what is widely seen as strong show of support for Abbas.
However the United States publicly disagreed with France, one of its closest allies, on late Tuesday.
"We obviously disagree with our oldest ally on this issue. They know that we disagree with them," State Department spokeswoman Victoria Nuland said. "But it's their sovereign decision to make, how to proceed."
She confirmed that if a vote goes ahead as planned in the UN General Assembly, the United States will vote against the Palestinian request, which Washington regards as "a mistake."
"We're focused on a policy objective on the ground for the Palestinian people, for the people of Israel, which is to end up with two states that can live peacefully next to each other," Nuland told journalists.
France is the first major European power to voice approval of the Palestinian move to upgrade its current permanent observer status, while Britain has said it has yet to decide on its position.
Over the last week, Abbas also received a rare show of support from the rival Palestinian nationalist movement, Hamas, which rules the Gaza Strip.
Until now, the Islamist movement had publicly opposed the bid, accusing Abbas of acting unilaterally and warning it would compromise Palestinian rights.
But this week, Hamas's exiled political chief Khaled Meshaal phoned Abbas to tell him that Hamas "welcomes the step of going to the United Nations for state observer status."
And shortly afterwards, Sami Abu Zuhri, a spokesman for Hamas's Gaza government, confirmed the movement's support for "any diplomatic step which will get something more for the Palestinian people."
But Abbas is aware there is likely to be a political backlash over his decision to return to the United Nations.
Israel is already weighing countermeasures in response to the UN bid, including freezing the transfer of tax and tariff funds it collects on their behalf and possibly cutting the number of work permits issued to Palestinians.
Some ministers have warned they could declare the 1993 Oslo peace accords void, and a policy paper at the foreign ministry even suggested "toppling" Abbas's Palestinian Authority.
But a spokeswoman for the ministry told AFP on Tuesday that Israel would most likely not take any punitive measures if the Palestinians merely upgraded their status, in what the Jewish state considered a largely symbolic act.
"Israel's reaction to the Palestinian move depends on what they choose to do," said Ilana Stein.
"If they use this resolution as a platform for confrontation, we will have to act accordingly," she said. "If that is not the case, we will not take any drastic measures."
Washington has repeatedly urged Abbas to drop the request, warning he risks losing US funding, notably around $200 million in development aid earmarked for the Palestinian Authority which is currently blocked in the US Congress.
"Obviously, if they take this step it's going to complicate the way the Congress looks at the Palestinians," State Department spokeswoman Victoria Nuland said this week.
It could also affect American financial aid to the United Nations under terms of a US law which prohibits funding international bodies that recognise a Palestinian state.
Abbas has repeatedly insisted that the bid is meant to complement efforts to achieve a two-state solution, not torpedo them.
"We don't want any confrontations with the United States or Israel. If we could start a dialogue or negotiations the day after the vote, we will."