The departure of British nationals from Gaza will likely take place “in stages over the coming days”, the UK Foreign Office has said.
The Rafah border crossing with Egypt is being opened for “controlled and time-limited periods” and to allow the seriously wounded to leave.
The first group of foreign nationals and injured Palestinians have been given permission to cross on Wednesday.
Some 200 British nationals are believed to be in Gaza.
Civilians in Gaza had largely not been able to leave the territory since 7 October following Hamas’s attacks on Israel, where more than 1,400 people were killed and at least 239 taken hostage.
The Hamas-run health ministry in Gaza says more than 8,700 people have been killed since Israel’s retaliatory bombing began.
Israel controls the air space over Gaza and its shoreline, and has strictly controlled the movement of people and goods.
The first ambulances carrying injured civilians from Gaza have now crossed into Egypt.
Some 500 people per day will be allowed to cross to the Egyptian side of the Rafah border.
A list of hundreds of names has been published by the border authority in Gaza, showing the dual and foreign nationals who should be allowed to leave through the crossing on Wednesday.
Among them are two British nationals who work for non-governmental organisations (NGOs). It is not known what day they will be leaving.
It follows talks between Prime Minister Rishi Sunak, Foreign Secretary James Cleverly and Middle East minister Lord Ahmad, and their counterparts in Egypt, Israel and Qatar.
The lists of those leaving will be agreed between the Egyptian and Israeli authorities, and relevant embassies will be informed in advance so they can prepare to receive their nationals.
Mr Cleverly said UK teams on the ground in Egypt were “ready to assist British nationals as soon as they are able to leave”.
“It’s vital that lifesaving humanitarian aid can enter Gaza as quickly as possible,” he added in a statement on X, formerly Twitter.
Western officials said a team had been deployed to Arish, a city some 25 miles (41km) away from Rafah, to “ensure we can provide the necessary medical, consular and administrative support needed” for British nationals.
Among the British nationals in Gaza are Scottish First Minister Humza Yousaf’s in-laws. He welcomed the opening of the border but said his wife’s parents remained trapped without clean drinking water and rapidly diminishing supplies.
Both Mr Sunak and Labour leader Sir Keir Starmer have called for humanitarian “pauses” in fighting to allow for aid to flow into Gaza.
Compared to a formal ceasefire, humanitarian pauses tend to last for short periods of time, sometimes just a few hours.
They are typically implemented purely with the aim of providing humanitarian support, as opposed to achieving long-term political solutions, according to the United Nations.