Al-Ahmad, who is also the head of Fatah delegation for the Cairo talks, said what was agreed upon two weeks ago under the auspices of Egypt is empowering the legitimate government to operate in accordance with its powers in accordance with the Basic Law in effect in the West Bank. Hamas leaders have said they would not disarm as long as Israel occupies Palestinian land.
Fatah's Palestinian Authority President Mahmoud Abbas told reporters that he welcomed the agreement.
The two sides began meeting in the Egyptian capital on Tuesday with the aim of ending the crippling decade-old split between the rival factions.
While details about the deal are still scarce, it appears that Fatah - the ruling party in the West Bank - will have more control over Gaza, run by Hamas since the split.
It has fought three wars with Israel since 2008 and the blockaded Gaza Strip has faced deteriorating humanitarian conditions.
"The legitimate government, the government of consensus, will return according to its responsibilities and according to the law", Fatah delegation chief Azzam Al-Ahmed said at the signing ceremony in Cairo.
Multiple previous reconciliation talks have failed.
But the move was seen as mainly symbolic, with Hamas still effectively in charge in the Palestinian enclave of two million people bordered by Egypt, Israel and the Mediterranean Sea.
Hamas has remained staunchly opposed to even discussing demilitarization, and in the past has called their military wing the "arms of the resistance" and argued "the resistance's weapons are legal".
Last week, Palestinian Authority prime minister Rami Hamdallah visited Gaza for the first time since 2015 and his ministers took formal control of government departments in the territory.
"We also agreed that the [Ramallah-based Palestinian] government would operate Gaza's Rafah border crossing with Egypt and all of Gaza's crossings with Israel", al-Ahmad added.