Middle East mediators have agreed a plan to channel aid directly to the Palestinians, bypassing the Hamas-led Palestinian Authority (PA).
Aid agencies have warned that Palestinians are getting poorer
The EU, UN, Russia and the US said they would set up a "temporary international mechanism" to channel the money for an initial three-month period.
Hamas welcomed the plan, but criticised moves to sideline the PA.
Separately, the Palestinians' only fuel supply is reported to have been cut off because of mounting PA debts.
Palestinian officials and Israel Radio said the Israeli Dor Energy company has halted deliveries, amid reports it is owed $27m.
Mujahed Salameh, director general of the Palestinian Petroleum Agency, said petrol and cooking gas would run out within 24 hours.
"There will be an economic catastrophe," Mr Salameh was quoted by Reuters news agency as saying.
"Many factories, bakeries and transport will stop working."
Sense of relief
The PA has faced a financial crisis since foreign aid was frozen after Hamas - regarded as a terrorist movement by the US and EU - won elections in January.
It has been unable to pay some 165,000 government employees for several weeks and the World Bank has warned of an imminent humanitarian crisis in the West Bank and Gaza.
On Tuesday, the so-called Middle East Quartet announced their plan to resume aid under a "temporary international mechanism" directly to the Palestinians rather than the PA.
The US also said it would separately give $10m (£5.4m) in aid to the Palestinians through medical and children's charities.
The BBC's Alan Johnson in Gaza says the news was greeted with relief by Palestinians on the streets.
Hamas also welcomed the promise of aid, but criticised attempts to bypass the PA.
"We appreciate every effort in order to help the Palestinian people by legal channels... and the legal channel is the Palestinian Authority, whether the presidency or the government," Palestinian Foreign Minister Mahmoud Zahar told reporters, the Associated Press news agency said.
Israeli Foreign Minister Tzipi Livni told Israel Army Radio the plan was acceptable to Israel.
"As far as we are concerned, the Quartet's decision to give further humanitarian support to the Palestinian Authority, bypassing the Hamas government, is definitely okay," she said.
The BBC's Laura Trevelyan in New York says the interim aid mechanism was agreed as it had become apparent that the suspension in foreign aid had not changed Hamas's policy.
But foreign donors do not want to completely remove the responsibility for paying the Palestinians from their government, our correspondent adds.
The EU's External Affairs Commissioner, Benita Ferrero-Waldner, said experts would meet in Brussels to work on the interim aid plan.
But, she said, it was "not an easy mechanism", which would take weeks rather than days to devise.
She told the BBC that responsibility for securing aid for the Palestinians rested with a range of parties.
These included Israel - which is withholding taxes from the Palestinians - the international community, the Arab nations and the Palestinians themselves.