The committee consists of 13 factions, including the ruling Fatah movement, Hamas, the Islamic Jihad, and left-wing parties. The committee is headed by legislator Ibrahim Abu-Najja.
Hamas and the Islamic Jihad, which rejected a request to join a national unity government, insisted on forming a national committee to observe the Israeli withdrawal from the Gaza Strip and northern West Bank.
"We were surprised when Abu-Najja contacted Hamas leadership and informed us that Abbas agreed to consider the follow-up committee as the one that will follow up the withdrawal," Saed Seyam, a senior Hamas official, told reporters.
Abu-Najja, secretary general of the committee, said in press statements that Abbas will meet with members of the committee in Gaza later on Thursday to officially inform them of his decision.
"The decision was taken after the approval of the Fatah's Central Committee during a meeting 10 days ago in (the Jordanian capital of) Amman," Abu-Najja said.
Israel is set to implement its unilateral disengagement plan in mid-August, which will see the withdrawal of all the 21 settlements in the Gaza Strip and four smaller ones in northern West Bank after almost four decades of occupation.