An Israeli official said on Thursday the money would be turned over to Abbas by the next day.
The transfer, which will help to ease the serious cash-flow crisis suffered by the Palestinian Authority, was promised by Olmert when he met with Abbas on December 23.
But it will not be used for salaries of government workers, who have not been fully paid since Hamas took office.
Nour Odeh, Al Jazeera's correspondent in Gaza, said: "Clearly this will go mostly to the private sector - this will be hard news for the public sector."
She said: "The $100 million is only a starting point for the Palestinian Authority, but its not nearly enough to end the financial crisis."
Hamas has criticised the Israeli restrictions on the money, after Israeli officials said they needed assurances the money would not reach Hamas.
Israel collects about $50 million in taxes from the Palestinians each month, which has contributed to a financial crisis for the Hamas-led Palestinian government.
"This is supposed to be spent according to Palestinian priorities. It is not for Israel to determine where it goes"
Samir Abu Aishah, Acting Hamas Finance Minister
Samir Abu Aishah, the acting finance minister for Hamas, said that the government should decide how the money is spent.
He said: "This is supposed to be spent according to Palestinian priorities. It is not for Israel to determine where it goes.
"We have no problem if that money goes through the president's office, but it must be spent in the areas in which they are needed, according to our priorities."
Abbas has been pushing Hamas to join his party in a moderate coalition government, hoping to end the international boycott against the Palestinian government.
On Saturday, he is scheduled to travel to Syria for talks with Khaled Meshaal, the exiled Hamas leader, in hopes of working out a deal.