The White Helmets fight fires and carry out repairs in war zones.
The UK, one of the nations requesting Israel's help, hailed the operation and will assist with resettlement.
Raed Saleh, the head of the Syrian Civil Defense, as the White Helmets are formally called, confirmed the evacuations took place but would not elaborate on the numbers of people who got out.
How did the operation come about?
Canada has offered to accept dozens of White Helmets and their families from Syria following a dramatic rescue over the weekend that was orchestrated by the Israeli military and personally encouraged by Prime Minister Justin Trudeau.
The latest deal for Quneitra was reached on Thursday.
It said they were transferred to a neighbouring country, which it did not identify.
The rescue workers and their families crossed out of Syria into the Israeli-occupied Golan Heights before arriving in Jordan.
White Helmets boss Raed Saleh said the evacuees had been encircled in the provinces of Daraa and Quneitra.
The U.S. State Department said in a statement that it welcomed the operation and renewed its call on "the Assad regime and Russian Federation to abide by their commitments, end the violence, and protect all Syrian civilians".
The U.S. statement said that "we deeply appreciate Israel's role in facilitating the transit of the White Helmets and their family members".
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"Refugees have set up tents just metres away from the Israeli-controlled Golan frontier, and early last week dozens risked walking over minefields to approach the border fence, some carrying white flags in an apparent attempt to cross to safety", the Guardian in England reported Saturday.
Jordan said on Sunday that it has taken in 800 Syrian White Helmets rescuers and their families from Israel and plans to transfer them to the United Kingdom, Canada and Germany.
Netanyahu, in broadcast remarks, said he would tell the envoys that "Israel insists on the separation of forces agreement between us and Syria being honored, as they were honored for decades until the civil war in Syria broke out".
White Helmets head Raed Saleh said the evacuees had arrived in Jordan after being "surrounded in a risky region".
He said the aid workers would remain at a "closed" location and that Britain, Germany and Canada had agreed to resettle them within three months. "We therefore took steps with the aim of affording that protection to as numerous volunteers and their families as possible".
"We pay tribute to the fearless and selfless work that White Helmets volunteers have done to save Syrians on all sides of the conflict". Damascus claims the White Helmets is linked with Jabhat al-Nusra (a terrorist organization outlawed in Russia) and is acting in its interests.
As towns have fallen, hundreds of thousands of people have fled their homes, and many, including members of the White Helmets, ended up in the shrinking pocket of rebel-held territory along the Israeli-held Golan Heights.
Numbering about 3,000 volunteers, they also carry out essential fix works. Around 200 have been killed.
The group was nominated for the Nobel Peace Prize in 2016 for its humanitarian efforts.
But Mr Assad's opponents see them as heroes for their rescue work in bombed, rebel-held cities.
President Assad said it used "humanitarian masks and umbrellas just to implement a certain agenda".