Hamas and Fatah agreed in 2014 to form a national reconciliation government, but the deal soon dissipated in mutual recriminations with Hamas continuing to dominate Gaza.
"We also extend our thanks and appreciation to President Abbas who had the desire and the real will to end the division and restore the unity of the brotherly Palestinian people", the statement read.
The two factions, the same source continued, had also agreed to allow a legal and administrative committee, drawn up earlier in Ramallah, to find solutions to longstanding problems - mostly related to salary shortfalls - faced by Gaza's Hamas-hired civil servants.
The meetings in Cairo are centred around implementing the 2011 Cairo Agreement between the two political parties, in hopes of ending the 10-year political schism.
He said the unity government would "run all institutions without exception", including all border crossings with Israel and in Rafah, Gaza's only access point with Egypt. Abbas has said he would not take over Gaza until Hamas gave up its weapons.
Abbas has tried numerous times without success to fix the rift, in part to counter Israeli assertions that peace negotiations are pointless because he can't ensure that any treaty will also hold in Gaza.
U.S. to Leave UN Body
It will establish an observer mission at the Paris-based organisation to replace its representation, the state department said. He said he has ordered Israeli diplomats to prepare Israel's withdrawal from the organisation in concert with the Americans.
Egyptian chief of intelligence, Khalid Fawzi, presided over the signing as Hamas' representative, Saleh al-Arouri, and Fatah's negotiator, Azzam al-Ahmed, signed on. Egypt has been brokering the reconciliation talks.
Repeated reconciliation attempts have failed since 2007.
Hamas does not recognise Israel and has fought three wars with the Jewish state since 2008.
The U.S. says it wants the Palestinian Authority to take control of Gaza again.
The new deal is understood to cover border crossing arrangements, Hamas' arsenal and the livelihoods of thousands of public servants.
Israeli Prime Minister Benjamin Netanyahu has warned Palestinians against "bogus reconciliations", and reiterated Tel Aviv's demand for the disbandment of Hamas's military arm.