The 25-page reconciliation pact calls for Palestinian presidential and parliamentary elections to be held on June 28.
Fatah had demanded that the legislative elections be largely proportional.
But Hamas insisted that a large part of the seats, at least 40 per cent, still be chosen through district representation.
Hamas won the last elections in 2006 when, for the first time, half the parliament seats were chosen through district representation.
The Egyptian compromise suggests that in the next poll, 75 per cent of the parliament seats be elected proportionally and 25 per cent via district representation.
The sides will not form a unity government as they had previously planned.
Instead, Hamas will continue to rule Gaza until the elections, while the Ramallah-based government of Salam Fayyad, the Palestinian prime minister, will continue to administer the West Bank.
A joint factional committee is to oversee implementation of the agreement.
The Egyptians hope to hold a formal signing ceremony of the document in Cairo on October 25.
A celebration was planned in late November at the end of the Muslim Eid el-Adha holiday.
The document also deals with the delicate issue of control over the Palestinian security forces.
About 3,000 Palestinian officers - members of all Palestinian factions - are to be trained in Egypt and Arab countries, as part of a rehabilitation of the security forces in the Gaza Strip.
The new force is expected to guard Gaza's border crossings.
Hamas had threatened not to sign the Egyptian proposal following Palestinian anger over the decision by Mahmoud Abbas, the Palestinian president and Fatah leader, to delay a UN vote on the Goldstone report.
The report accuses mainly Israel - but also Hamas - of having committed war crimes during the 22-day war that killed 1,400 Palestinians and 13 Israelis last year.