The strikes, in collaboration with the U.S. and France, are in response to an alleged chemical attack on the Syrian town of Douma last week.
British Prime Minister Theresa May said on Saturday she had authorized British forces to conduct precision air-launched cruise missile strikes on Syria to degrade its chemical weapons capability, saying there was no alternative to military action.
"We are prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents", the USA president said in a televised address.
The British PM said the attack was specifically a reaction to the use of chemical weapons, and was not about a regime change.
Alexander Yakovenko, the Russian ambassador to London, said the White Helmets, a British-funded civil defense force, were responsible for staging fake chemical attacks.
President Vladimir Putin has said Russian Federation will call an emergency session of the UN Security Council over air strikes on Syria.
"We have hit a specific and limited set of targets", she said.
"This collective action sends a clear message that the global community will not stand by and tolerate the use of chemical weapons", May told a press conference.
"This is the first time as prime minister that I have had to take the decision to commit our armed forces in combat - and it is not a decision I have taken lightly", she said.
"I think it is right that the global community has come together and said we will not accept this", she added.
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The Ministry of Defence (MoD) said that four RAF Tornado jets were deployed to launch missiles at a Syrian military facility.
Speaking in Downing Street, May said the military strikes should be a "warning to Russia" before holding the Syrian government accountable for the chemical attack.
May added Britain and its allies had sought to use every diplomatic means to stop the use of chemical weapons, but had been repeatedly thwarted, citing a Russian veto of an independent investigation into the Douma attack at the U.N. Security Council this week.
"Very careful scientific analysis was applied to determine where best to target the Storm Shadows to maximise the destruction of the stockpiled chemicals and to minimise any risks of contamination to the surrounding area", the ministry said.
British Prime Minister, Theresa May, is "confident" that the air strikes carried out by all three countries have been successful, according to the BBC.
Besides Trump, French President Emanual Macron said in a statement that they also could not tolerate the normalisation of the use of chemical weapons.
May held an emergency cabinet meeting to discuss possible action on Thursday and there had been calls for the British parliament to be consulted before any air strikes.
Mrs May had earlier explained that there was no alternative to military action.
"Bombs won't save lives or bring about peace", Jeremy Corbyn, leader of the main opposition Labour Party, said in a statement. "This legally questionable action risks escalating further".