Nabil Shaath, a senior adviser to Palestinian President Mahmoud Abbas, told journalists in the West Bank city of Ramallah that Hamdallah would meet Hamas officials in Gaza City and assert the government's control over ministries as a first step towards implementing a larger agreement.
"We await the first steps on the ground. We want to see Mr Hamdallah received by Hamas, the door to all the ministries open," he said. "That really could happen in the next 24 hours."
Hamas announced on Sunday it had agreed to demands by Abbas' Fatah party to dissolve what is seen as a rival administration in Gaza while saying it was ready for elections and negotiations towards forming a unity government.
Abbas' internationally recognised Palestinian Authority (PA) is located in the Israeli-occupied West Bank, but it has had no control in Gaza for a decade - after Hamas seized the territory in a near civil war in 2007.
Hamdallah has not visited Gaza since 2015, and a previous attempt at a unity government fell apart that year, with the two sides exchanging blame.
The head of the Arab League on Monday hailed the steps taken by Hamas and called for full reconciliation.
Ahmed Aboul Gheit "welcomes the important positive developments" regarding "ending the division" between the Palestinian factions, the Cairo-based organisation's spokesman Mahmoud Afifi said in a statement.
In recent months Abbas has sought to squeeze Hamas by reducing the power supply to the Gaza Strip, with the two million residents receiving only three or four hours of electricity per day as a result.
Abbas had also reduced the salaries of some employees in Gaza, while the number of Gazans receiving PA permits to travel for medical care has declined.
Hamas on Monday called for the measures to be reversed.
In a statement, Hamas called on Abbas to "take urgent steps to cancel all his punitive decisions and measures against our people in the Strip".
Shaath said Abbas wanted to reverse the punitive moves, but he did not give a timetable.
"When the president supported these economic measures [against Gaza] he said they will stop immediately once the self-rule governance of Hamas ends and the consensus government takes place. He didn't put any other conditions whatsoever," said Shaath.
Source: News agencies