Israel radio reported that all the outstanding issues had already been resolved in principle. A Palestinian minister, Jamil Tarifi, told waiting journalists at the Laromme hotel in West Jerusalem that: "We expect an agreement tonight. I hope so."
The terms were due to be sealed at a summit meeting today, between the Israeli Prime Minister, Benjamin Netanyahu, and the Palestinian leader, Yasser Arafat.
In a surprise move, the American mediator, Dennis Ross, drove to Gaza last night for a further session with Mr Arafat and his deputy, Mahmoud Abbas. Mr Ross said: "There is work going on. There is still a lot of work to be done."
An Israeli official insisted, however, that the two sides were "very close to an agreement", and that only "the fine print has not been finalised yet".
The Israeli Defence Minister, Yitzhak Mordechai, insisted: "As the Christians say, it will be a happy Christmas."
The Israeli redeployment is nine months overdue. It was postponed after "Islamist" suicide bombings killed dozens of Israelis in February and March. The right-wing Likud government, which came to power in June, then insisted on strengthening the security guarantees for the 450 Jewish settlers living in the old town of Hebron amid 150,000 Arabs.
The agreement, brokered by the United States, will restore much of the goodwill which has been dissipated by Mr Netanyahu's patronising approach towards the Palestinians, and by the bloody exchanges of fire between Israeli troops and Palestinian police in September. It will open the way to further Israeli withdrawals under the interim Oslo accords, and to negotiations for a definitive settlement of the Israeli-Palestinian conflict.
As a confidence-building measure, Israel yesterday increased the number of permits for Palestinian day labourers to work in Israeli farms, factories and building sites from 42,000 to 50,000.
The final push towards the Hebron agreement was given by the US mediator, Dennis Ross, during a long night of talks with the Israeli and Palestinian teams on Sunday. Technical teams then met again yesterday. Mr Ross flew to Cairo to update the Egyptians.
The level of the talks was raised in the afternoon, when Mr Netanyahu and Mr Arafat's deputy, Mahmoud Abbas, joined the negotiators. The full teams met in the historic King David hotel in Jerusalem for two hours. Then Mr Netanyahu and Mr Abbas talked tete-a-tete for about half an hour.
Both sides later reported substantial progress. Mr Abbas reported back to Mr Arafat in Gaza. Mr Netanyahu briefed Mr Mordechai and his foreign minister, David Levy.
Although the details were still under wraps, the parties are believed to have agreed on a main draft and accompanying letters. There is expected to be a United States letter of guarantee.
According to unconfirmed Israeli reports, Israel will withdraw in stages from a disputed road linking the Arab and Jewish parts of town. In return, the Palestinians will widen a buffer zone around the Jewish enclaves. New regulations are said to have been agreed on the arms that the two security forces will carry, as well as on their respective freedom of operation.