The decision for the Palestinian Authority to leave the area was made in response to Hamas's "measures."
A resident of Gaza City said he hoped that he will be able to travel abroad for studies.
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.
Following her death, Diab has been described on Palestinian social media as "the martyr of the siege on Gaza," who died as a result of the closure of all the border crossings to Gaza.
Video obtained by Reuters showed what the cameraman said to be an Egyptian warplane flying over Gaza.