He went on to say that, according to the terms of the deal, Presidential Guard units linked to the Ramallah-based Palestinian Authority (PA) would be deployed along Gaza's southern border with Egypt no later than November 1.
Yahya Sinwar, Hamas's acting chief in Gaza, for his part, congratulated Abbas on the watershed agreement.
Celebrations broke out in the Gaza Strip after the announcement of the deal, with residents waving flags of Egypt, Palestine, Fatah and Hamas. Hamas has said it hopes that by giving back power to the Palestinian Authority, life in Gaza can improve.
Egyptian President Abdel-Fattah el-Sissi said on Sunday the Egypt-backed reconciliation talks between the PA and Hamas are "preparation" for an Israeli-Palestinian peace deal.
Fatah officials said the two sides agreed that the Palestinian Authority would take over responsibility for Gaza's border crossings no later than November 1 and that full governing responsibilities would be handed over to the Palestinian Authority by the beginning of December.
The deal includes 3,000 members of the West Bank-based Palestinian Authority's police force redeploying to Gaza, a member of the negotiating team told AFP on condition of anonymity.More news: Gators football team goes full reptile with green scaly uniforms
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.
He added that sanctions taken by Abbas against Gaza will also soon be lifted. Hamas and Israel fought three devastating wars over the past decade.
Al-Ahmed highly appreciated the Egyptian role and keenness to achieve Palestinian reconciliation, stressing that Egypt is the sponsor of the Arab national security, including the Palestinian security.
A permanent opening of the Rafah crossing would mean an end to the crippling Gaza border blockade which prevents free trade and bars the vast majority of Gaza's 2 million people from leaving the territory.
There was no indication that an understanding had been reached on the fate of Hamas's armed wing, a sticking point which analysts have said could yet scupper reconciliation efforts.