The Foreign Office is expected to help resettle the White Helmets and their families.
Jordan had originally said 800 Syrians were evacuated and Jordanian Foreign Minister Ayman Safadi tweeted on Sunday that the original agreement was for 800 but that they later settled at 422.
How did the operation come about?
More than 20,000 civilians have fled bombardment on the IS-held corner on the border with Jordan and the Israeli-occupied Golan in the past 24 hours, fleeing into regime-held areas, said the Syrian Observatory for Human Rights monitor.
Their volunteers have gone into war-stricken areas, searching for survivors, winning them support from many countries, including the United States.
How was it carried out?
The UK had backed an global effort to rescue members of the group and their families from the frontier with the Israeli-occupied Golan Heights.
"Several days ago, U.S. President Trump contacted me, as did Canadian Prime Minister Trudeau and others, and requested that we assist in evacuating hundreds of White Helmets from Syria", Netanyahu said in Hebrew during an online address. But Israel has said it will not allow the refugees to enter Israel.
The Israeli military said that overnight it had completed "a humanitarian effort to rescue members of a Syrian civil organisation and their families.due to an immediate threat to their lives". But large parts of the country remain out of his hands, held by rebels, Turkey, or Kurdish forces backed by the United States. Although it has sent aid into Syria and has provided medical treatment to thousands of Syrians who reached the Golan Heights frontier, the Israeli military said its actions did not reflect a change to Israel's non-intervention policy in Syria's war, where all the warring parties are considered hostile.
"The [Jordanian] government gave the permission after Britain, Germany and Canada made a legally binding undertaking to resettle them within a specified period due to a "risk to their lives", the kingdom said.
The Government said the United Kingdom would provide protection to "as numerous volunteers and their families as possible".
British Foreign Secretary Jeremy Hunt and International Development Secretary Penny Mordaunt confirmed the operation in a joint statement that praised the "brave and selfless work" of the group.
They also became witnesses to the numerous war crimes committed by Syrian President Bashar Assad and the Russian military as both deliberately targeted civilian structures in bombing raids.
He wrote on Twitter that the White Helmets will release an official statement on the matter on Monday.
More than 2,500 people, among them fighters from Islamist groups who have rejected the deal, left on Friday headed to opposition areas in northern Syria.
Numbering about 3,000 volunteers, they also carry out essential fix works.