Senior Hamas leader Saleh al-Arouri (left) sits next to Fatah's Azzam al-Ahmad as they sign a reconciliation deal in Cairo on Thursday.
According to the deal, the Palestinian consensus government would fully take over running the daily affairs in the Gaza Strip from the hands of Hamas.
But, after the reconciliation deal thousands of Palestinians now look forward to better times ahead.
Although Mr Blair did not elaborate on the nature of the British Government's "informal" contact with Hamas, he appeared to be referring to talks between MI6 and Hamas representatives to secure the release of a British journalist kidnapped in Gaza in 2007.
Palestinian Authority President and Fatah head Mahmoud Abbas hailed Thursday's agreement as a "final agreement to end the division" - though many key issues remain to be resolved and previous reconciliation attempts have repeatedly failed.
Also as part of the agreement, the Palestinian Authority can not take any new steps regarding Israel.
Egypt, which hosted a series of meetings over the past few days between both parties, invited the Palestinian factions that signed the 2011 accord to hold their upcoming meeting on November 21, 2017, in Cairo.
The deal comes a month after Hamas dissolved the committee which runs the Gaza Strip and said it was willing to work towards reconciliation with its West Bank rivals. The reports also said the Palestinian Authority would seek to merge Hamas' police officers in Gaza with the Palestinian security services.
According to the agreement, the Western-backed Palestinian Authority will resume all governing responsibilities in Gaza no later than December 1.
But one central issue has yet to be discussed: the fate of Hamas' militant wing and cache of rockets and weapons.
Islamist movement Hamas is blacklisted as a terrorist organization by the United States and the European Union.
He added that President Recep Tayyip Erdogan had always supported the talks, and had held meetings with the Hamas and Fatah leaders.
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.