The Israeli military said the evacuation came at the request of the U.S. and a number of European countries.
The White Helmets operate only in rebel-held areas, although they say they are non-partisan.
'The civilians were subsequently transferred to a neighbouring country, ' it said without elaborating.
Supporters of President Bashar al-Assad, and his ally Russian Federation, say the White Helmets support the rebels and also have links to jihadist groups. Safadi, Jordan's foreign minister, said in a tweet that his government approved the evacuation after a pledge from Britain, Germany and Canada that the evacuees will be resettled in three months.
A readout of a phone call between the two was released by the Prime Minister's Office on Saturday.
"The White Helmets have saved over 115,000 lives during the Syrian conflict, at great risk to their own".
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The group, which often publish dramatic videos of themselves digging civilians out of rubble, has been lauded for their heroism but have also been criticized by supporters of Syria's government and its ally Russian Federation, who accuse them of being a front group for Al-Qaeda or acting in Western interests.
"Israel continues to maintain a non-intervention policy regarding the Syrian conflict and continues to hold the Syrian regime accountable for all activities in Syrian territory".
Since the offensive began, Jordan said it will not open its borders to the newly displaced Syrians. They have reached Jordan, thank God.
"While in Jordan, UNHCR in close collaboration with the involved governments, is supporting their temporary stay in anticipation of their onward relocation to third countries", the statement said.
The Syrian army and its allies have made advances against Daesh terrorists in the country's southwest near the Israeli-occupied Golan Heights.
A Jordanian foreign ministry spokesman confirmed to Reuters that the civilian workers were transferred to his country.
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"Humanity dictates that many of these fearless first-aiders should now find protection and refuge, some of them in Germany", it quoted German Foreign Minister Heiko Maas as saying.
Britain said the operation was possible due to the joint diplomatic efforts, hailing the efforts of the White Helmets volunteers to save lives in opposition areas. It was not immediately clear if that amounted to the same 50 people.
"The White Helmets have witnessed vicious atrocities committed by the Assad regime and its backers", she said in a statement, adding "Canada has been a key partner of the White Helmets and is proud to have provided funding to support their emergency training and to increase the number of women White Helmets".
Russia's embassy in the Netherlands welcomed the White Helmets' departure.
Both Moscow and Damascus have accused the White Helmets of staging rescue missions and chemical attacks to blame on the government.
Also, the rebel groups in the areas of "Muzayrib" and "Yadouda" in rural Daraa continued to hand over their weapons to the Syrian army, including 7 tanks, 3 armored vehicles and various equipment.
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