Jordan later confirmed that 422 Syrian citizens had crossed its border, and that they would now be resettled as refugees in several Western countries.
Israel is on high alert as Syrian President Bashar al-Assad regains ground from rebels in the southwest of the country, bringing his forces close to the Israeli-occupied Golan Heights.
"Fantastic news that we - United Kingdom and friends - have secured evacuation of White Helmets and their families - thank you Israel and Jordan for acting so quickly on our request", tweeted British Foreign Secretary Jeremy Hunt.
Founded in 2013, the Syria Civil Defense, popularly known as the White Helmets, is a network of first responders that rescues people wounded by air strikes, shelling or explosions in rebel-held areas.
The group have been lauded for their heroism by the US, UN, and others, but have 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.
But, that's resulted in them being identified with opposition forces, and therefore a target for the Syrian army.
Canadian Foreign Minister Chrystia Freeland said her country was working with Britain and Germany "to ensure the safety of White Helmets and their families".
It was the second suspected attack in a week by Israel on army installations that the Syrian opposition and Western intelligence sources say have an Iranian military presence.
They had fled as a Syrian government offensive in the south-west of the country intensified earlier this summer.
On Saturday, more than 400 rescuers and their family members were evacuated from Syria's Quneitra province through Israel to Jordan, after the rebels surrendered the last areas they held in the southwestern province to the government.
"This has uncovered the support provided by these states to the terrorist groups in their aggression against the Syrians and in destroying the infrastructure in Syria under false pretexts".
The statement from spokeswoman Heather Nauert also called on Syria's government and its ally Russian Federation "to abide by their commitments, end the violence, and protect all Syrian civilians, including humanitarians such as the White Helmets, in areas formerly part of the southwest de-escalation zone and throughout Syria".
The rockets fell inside Syrian territory and were part of internal fighting, a military statement said.
The Syrian government managed to get full control over a strategic territory at the border with Jordan following the operation. Jordan hosts at least 650,000 registered Syrian refugees, according to the United Nations, but Amman said a similar number of undocumented Syrians are also in the kingdom.
Israelis involved in the rescue operation told Hadashot news that it was one of the most emotional efforts to help Syria to date.
The regime considers the White Helmets a "terrorist" organisation because it works in areas controlled by its opponents.
El Deeb reported from Beirut.