A senior aide to Abbas, Saeb Erekat, said the funds would go to humanitarian projects and the private sector, but declined to say whether any would go towards boosting Abbas's security.
The transfer was promised by Olmert when he met 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.
Fawzi Barhoum, a
Hamas spokesman, criticised that decision not to allocate the funds for salaries.
"The dangerous thing about what happened was first it bypassed the Palestinian legitimate government and the ministry of finance, and second it has given the occupation the right to determine where the money should go," he said.
The US has been pressing Israel to strengthen Abbas of Fatah in his rivalry with Hamas, which has been building up its own "Executive Force".
Israel collects about $50m in taxes from the Palestinians each month, which has contributed to a financial crisis for the Hamas-led Palestinian government.
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 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.
However, at a press conference with Javier Solana, the European Union foreign policy chief, he would say only that he would meet "numerous Palestinian figures" in the Syrian capital.
Palestinian government workers signed an agreement over the weekend to end a strike over unpaid wages, but it was unclear where Abbas would secure the funds to start paying salaries.