Among the first to cross were two ambulances ferrying patients from the hitherto-blockaded Gaza Strip for treatment in Egypt, as well as a minibus carrying a dozen visitors.
A total of around 200 Gazans had crossed by early afternoon.
"I've been waiting for this for years," said 25-year-old Samah al-Rawagh, one of the first 200 to leave the densely populated Palestinian enclave.
|Palestinian men remove sacks of gravel smuggled into the Gaza Strip through a tunnel under the Egypt-Gaza|
The crossing will be open to people for eight hours a day from 9:00 am, apart from holidays and Fridays, giving Gazans a gateway to the world as Rafah is the only crossing which does not pass through Israel.
Under the long-awaited change, which excludes the flow of goods, people under the age of 18 or older than 40 require only a visa to pass, but men between 18 and 40 still need security clearance, officials said.
Jamal Nijem, 53, whose wife and daughter live in his spouse's native Egypt, was among hundreds who flocked to the border post, but he was unsure whether he would be allowed to cross.
"I came here three years ago to rejoin my family but my Egyptian residency permit had run out because of frequent closures of the crossing, and the security services barred me from going back," he said.
Commercial traffic will continue to have to pass through border points with Israel to enter the impoverished territory.
According to an official in charge of administrative procedures on the Palestinian side of the terminal, "the process is going without a hitch, and we are providing the facilities for travellers to pass quickly and comfortably."
On the Egyptian side, an official said: "We are going to do everything possible to ease the passage of our Palestinian brothers, and we hope procedures will be simplified further in due course."
Aman Mahdi, 21, said she hopes her husband will be able to accompany her to Malaysia for medical treatment.
"I've been trying in vain for four months to travel. I am registered, but there have not been any concrete results due to a lack of coordination with the Egyptian authorities. I hope this time we can finally leave," she said.
Egyptian Foreign Minister Nabil al-Arabi announced in April that the crossing would reopen permanently, stressing this would help ease the blockade imposed by Israel.
The border has remained largely shut since June 2006 when Israel imposed a tight blockade on Gaza after Palestinian militants snatched Israeli soldier Gilad Shalit, who is still being held.
The blockade was tightened a year later when the Islamist movement Hamas seized control of the territory, ousting forces loyal to the Western-backed Palestinian Authority.
The United Nations has called the blockade illegal and repeatedly demanded it be lifted.
The decision to permanently reopen the Rafah crossing came more than three months after former Egyptian president Hosni Mubarak resigned under pressure following 18 days of massive street protests against his rule.
It was hailed by Hamas and the European Union, but Israel has greeted the news with trepidation.
Hamas spokesman Fawzi Barhum said on Thursday the move was "a courageous and responsible decision which falls in line with Palestinian and Egyptian public opinion."
The European Union said it was in consultations with Egypt, the Palestinians and Israel about returning its team of advisers to monitor activity along the frontier.
But Israel expressed concern, with Home Front Defence Minister Matan Vilnai telling public radio it would create "a very problematic situation."
The opening follows an April 27 unity accord between rival factions Hamas and the Fatah party of Palestinian Authority leader Mahmud Abbas that was signed in the Egyptian capital.
Israeli NGO Gisha, which campaigns for freedom of movement for Palestinians, said that over the past year an average of 19,000 people a month used the crossing, just 47 percent of the number who used it in the first half of 2006.