A first group of injured evacuees entered Egypt in ambulances, Egyptian media and a source at the border said at around 0935 GMT.
Israel responded with a total blockade of Gaza, heavy bombardment and a ground operation after Hamas fighters attacked southern Israel on Oct. 7.
A Palestinian border authority source and two Egyptian security sources said 81 injured people would enter Egypt for treatment on Wednesday.
In addition, up to 500 foreign passport holders will pass through the Rafah crossing on Wednesday, an Egyptian security source said, adding that about 200 people were waiting on the Palestinian side.
A second source with knowledge of the deal said there was a list of up to 500 who would leave Gaza but not all were expected to make it out on Wednesday.
Medical sources in Egypt's Sinai region, which borders Gaza, said a field hospital of four tents, each containing 20 beds, and 12 medical caravans had been set up in Sheikh Zuweid, 15km (9 miles) from Rafah.
Hospitals in Sheikh Zuweid and Al-Arish, a town a little further away, were also preparing to admit Gazan patients, with more difficult cases expected to be sent further out to Ismailia, the sources said.
A source at the border said 40 ambulances were at the crossing to take part in the evacuation operations.
In addition, 70 aid trucks were in the Rafah area, going through the process of checks required before they can go into Gaza, under an existing agreement with Israel.
The Hamas attack on southern Israel on Oct. 7 killed about 300 soldiers and 1,100 civilians, according to Israeli figures, and more than 200 hostages were taken.
At least 8,525 Palestinians, including 3,542 children, have been killed in Israeli strikes on Gaza since Oct. 7, according to the health ministry in the Hamas-run Gaza Strip.
The Rafah crossing, controlled by Egypt, is the main entrance and exit point to Gaza from Egypt and is in a region tightly controlled by the Egyptian military, which battled an Islamist insurgency there that peaked after 2013 and has now been largely suppressed.
With Egypt wary of insecurity near the border with Gaza, only people who have obtained security clearance from Egyptian authorities are allowed close to the Rafah crossing.
(Reporting by Yusri Mohamed in Ismailia, Ahmed Mohamed Hassan and Nafisa Eltahir in Cairo, Nidal al-Mughrabi in Gaza and Maya Gebeily in Beirut; Writing by Estelle Shirbon; Editing by Janet Lawrence)
