Egypt last opened the crossing more than two weeks ago.
Egypt tends to open the frontier temporarily a few times a year, usually with short notice and little explanation.
A resident of Gaza City said he hoped that he will be able to travel abroad for studies.
An Egyptian-brokered reconciliation deal last month formally restored Palestinian President Abbas's administrative control of Gaza.
The handover follows the conclusion of a reconciliation deal in October between the two Palestinian rival factions.
How will this impact Gaza border crossings with Egypt and Israel?
Egyptian intelligence is reportedly making the opening of the crossing conditional on security in the Sinai peninsula.
Since the ouster of Egyptian president Mohamed Morsi of the Muslim Brotherhood in 2013, Cairo has seldom opened the Rafah crossing.
Among those reportedly crossing were MP's and other political figures as well as academics.
Hamas refused to admit responsibility in Sinai security incidents, Al-Ahram says.