The White Helmets operate only in rebel-held areas, although they say they are non-partisan.
Britain is among the countries that will take in some of the 800 people removed overnight from Syria by Israeli forces.
Russian Federation and Syria must hunt down and prosecute members of the White Helmets for "war crimes", Syria's Grand Mufti has said shortly after Israel "evacuated" a large number of the group's members at the request of the United States and Canada.
Canada's foreign minister Chrystia Freeland said: "Canada, working in close partnership with the United Kingdom and Germany, has been leading an worldwide effort to ensure the safety of White Helmets and their families".
The Jordanian Foreign Ministry said Britain, Germany and Canada had initially agreed to welcome around 827 rescuers and their relatives but eventually settled on 422.
They are viewed as heroic, courageous and selfless rescue workers who've saved hundreds of lives, through the brutal course of Syria's war. "I therefore authorized their transfer via Israel to other countries as an important humanitarian gesture", Netanyahu said.
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The U.S. State Department welcomed the rescue of "these courageous volunteers" and cited the United Nations, Israel, and Jordan for helping with the operation.
The rescue workers have been lauded in the West for their heroism but the Syrian regime accuses the group of being a propaganda tool for the West and aligned with militant groups, an accusation lacking in evidence.
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.
Israel said on Saturday that it maintains a "non-intervention policy" when it comes to the conflict in Syria.
Another source familiar with the situation said Islamic State had actually been able to expand its territory over the last 20 hours by seizing at least 18 villages abandoned by other rebels under the banner of the Free Syrian Army (FSA). Evacuation plans were accelerated after last week's North Atlantic Treaty Organisation summit in Brussels.
Western powers have accused Syria of attacking rebel-held areas with illegal chemical weapons.
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The deal brings the area back under government control and lets Syrian army brigades return to where they were stationed before Syria's seven-year-old conflict - posts near a 1974 demilitarized zone with Israel on the Golan frontier.
More than 650,000 Syrian refugees are registered with the UN High Commissioner for Refugees (UNHCR) in Jordan but the kingdom says it hosts 1.3 million Syrian refugees. Some 300,000 have been displaced by the fighting, with only a few thousands opting for evacuation to Idlib, which is expected to be the target of the next government offensive.
The group was nominated for the Nobel Peace Prize in 2016 for its humanitarian efforts.
The White Helmets have financial backing from the U.S., Britain, and other nations.
El Deeb reported from Beirut.
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