The opening of the schools on August 29 had been in doubt after the United Nations Relief and Works Agency for Palestinian refugees (UNRWA) said it lacked funds to pay the 22,000 teachers in its educational network in the Gaza Strip, the West Bank and east Jerusalem, and Jordan and Syria.
UNRWA said students will return to its 711 schools on time though it still did not have enough money to fund them for a full school year.
UN officials said the agency needed more than $200 million from other contributors to cover its deficit after the US aid cuts.
US President Donald Trump said in January he would scale back aid to the Palestinians unless they cooperated with his plans to revive peacemaking with Israel. Those peace efforts stalled in 2014.
At a specially convened session of the UNRWA Advisory Commission in Amman, Commissioner-General Pierre Krahenbuhl said that since the beginning of the year the agency had received $238 million in additional contributions after a funding drive but was not "out of the woods".
"We currently only have funding to run the agency's services until the end of September," Krahenbuhl said in a statement. "We need a further $217 million to ensure that our schools not only open but can be run until the end of the year."
The agency, the oldest and largest UN relief program in the Middle East, provides health care, education and social services to millions of Palestinians in the West Bank, the Gaza Strip, Jordan, Syria and Lebanon.
Israel complains that the organization grants Palestinian refugees special status by counting descendants of Palestinians who were either forced to leave or fled during the 1948 War of Independence.
By using this unique categorization which no other refugee in the world is afforded, Israel says that UNRWA is responsible for exacerbating, rather than solving, the problem.
The body's edcuational facilities have also been used in the past for Hamas terror purposes.
Last October, it was reported that UNRWA discovered a Hamas attack tunnel underneath one of its schools in Gaza.
In January, Trump tweeted "we pay the Palestinians HUNDRED OF MILLIONS OF DOLLARS a year and get no appreciation or respect. They don't even want to negotiate a long overdue peace treaty with Israel." The US State Department has said the agency needed to make unspecified reforms.
Israel has accused UNRWA of favouring Palestinians and welcomed Trump's move.