The strikes targeted military bases near the capital Damascus and the city of Homs, in response to last week’s alleged chemical attack on the Syrian town of Douma.
Defence Secretary Gavin Williamson said it had been a “highly successful mission”.
Syrian state media called the strikes a “violation of international law”.
Prime Minister Theresa May said there was “no practicable alternative to the use of force”.
Mr Williamson added the UK, France and America had played an important role in “degrading the ability of the Syrian regime to use chemical weapons”.
The Ministry of Defence said Storm Shadow missiles were launched by four RAF Tornados at a former missile base 15 miles west of Homs, where it is thought the Assad regime is stockpiling items used to make chemical weapons.
A spokesperson added the facility was “located some distance from any known concentrations of civilian habitation” and scientific analysis was used to “minimise any risks of contamination to the surrounding area”.
In a statement Mrs May said that the Syrian regime had demonstrated a “persistent pattern of behaviour” when it came to the use of chemical weapons, that “must be stopped”.
The four British Tornado Jets took off in the early hours of this morning here from RAF Akrotiri in Cyprus. Each was armed with a Storm Shadow missile.
The cruise missile is 5m (16ft) long and has a range of 300 miles. They had already been programmed to find their target using GPS.
The four Tornados fired the missiles well away from Syrian airspace out of range of the regime’s air defences and then they all returned safely.
The Ministry of Defence has described the action as “proportionate”. While the UK might appear to have played a minor role in these strikes the defence secretary Gavin Williamson said it was part of a united response that sent a clear message to President Assad.
“We have sought to use every possible diplomatic channel to achieve this,” the prime minister said.
“This is not about intervening in a civil war. It is not about regime change.
“It is about a limited and targeted strike that does not further escalate tensions in the region and that does everything possible to prevent civilian casualties.”
Foreign Secretary Boris Johnson welcomed the news, saying the “world is united in its disgust for any use of chemical weapons, but especially against civilians”.
He said the military strikes were targeting “major chemical weapons facilities in Syria”.
‘Chemical weapon stockpile’
The Ministry of Defence (MoD) said that the four RAF Tornados launched Storm Shadow cruise missiles at a Syrian military facility.
Prime ministers don’t choose the decisions that face them. But they have to judge which way to jump.
In 2013, Theresa May’s predecessor tried and failed to get approval for military action against President Assad. There was international alarm, then as now, about his suspected use of chemical weapons.
But MPs rejected David Cameron’s plan and he didn’t try again to persuade Parliament it was necessary.
The former missile base was assessed to have been used by the Syrian regime to “keep chemical weapon precursors stockpiled in breach of Syria’s obligations under the Chemical Weapons Convention,” the MoD said in a statement.
The US Russian embassy Twitter account called the action “unacceptable and inadmissable”.
Mr Williamson said that British and Russian relations were at a low point.
Syrian state media said the air strikes were “a flagrant violation of international law”.
The official Sana news agency cited an unnamed source as saying: “When terrorists failed, the USA, France and Britain intervened and committed aggression against Syria.
“The American, French and British aggression against Syria will fail.”
Scotland’s First Minister Nicola Sturgeon said Mrs May had not answered how the action, “taken without parliamentary approval, will halt their [Syria’s] use” of chemical weapons “or bring long term peace”.
The Tornado has been one of the mainstays of the RAF since first entering service in 1980 and the aircraft were used to enforce no-fly zones in Iraq.
It is mainly used as a strike or attack aircraft.
Weapons such as the Storm Shadow cruise missile mean that the Tornado can hit targets from a significant distance. The MoD describes the missile as being designed for “long range, highly accurate, deep penetration” against enemy command and control bunkers. It is fired from a Tornado GR4.
Tornado GR4s are also equipped with Brimstone missiles, an effective anti-armour weapon and can also be used for all-weather, day and night tactical reconnaissance.>