The crossing is opposite Israel's new Kerem Shalom crossing.
A security official, speaking on condition of anonymity because he is not authorised to speak to the media, said on Wednesday the building and its facilities would be completed in 90 days.
Right now the site is just empty land, in contrast to Kerem Shalom across the border.
Initially, Egypt intends to use the crossing for commercial trucks delivering goods to Gaza and Israel, and it will discuss other issues, such as the passage of people, later.
Currently, commercial drivers use the Al-Awga crossing about 100km away.
People wanting to pass between Egypt and Gaza were using the Rafah border crossing, but Israel closed that when it pulled out of the Gaza Strip last month, and said it would be closed for six months to allow for new security and customs arrangements.
Israeli defence officials said in late September that Palestinians would soon be able to use the Kerem Shalom border crossing.
But Palestinians insist on free access in and out of Gaza through Rafah, with no Israeli presence, and object to the Kerem Shalom option.