Britain's defense ministry said initial indications were that the precision weapons and meticulous target planning had "resulted in a successful attack".
"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 Western missile strikes demonstrate the volatile nature of the Syrian civil war, which started in March 2011 as an anti-Assad uprising but is now a proxy conflict involving a number of world and regional powers and a myriad of insurgent groups.
May also spoke to Trump and French President Macron, and they agreed the strikes had been a success, Downing Street said.
"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.
"The facility which was struck is located some distance from any known concentrations of civilian habitation, reducing yet further any such risk", the MoD said in a statement.
"While this action is specifically about deterring the Syrian regime, it will also send a clear signal to anyone else who believes they can use chemical weapons with impunity", May said.
"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".
"I have done so because I judge this action to be in Britain's national interest".
May referred to last month's nerve agent attack on former spy Sergei Skripal and his daughter in the English city of Salisbury, which Britain has blamed on Russian Federation.
"We can not allow the use of chemical weapons to become normalised - within Syria, on the streets of the United Kingdom, or anywhere else in our world", she said.
Many politicians in Britain, including some in May's own Conservative Party, had called for parliament to be recalled from a break to give authority to any military strike.
Former prime minister David Cameron lost a parliamentary vote on air strikes against Assad's forces in 2013 when 30 Conservative lawmakers voted against action, with many Britons wary of entering another conflict after interventions in Iraq, Afghanistan and Libya failed to bring stability to the region.
Speaking from the White House on Friday, president Donald Trump announced the military action, and said its intention was to degrade Syrian chemical weapons capabilities.
Last week almost 75 people were killed in Douma after the Bashar's regime launched a poisonous gas attack in the region.
She said nearly a century of global aversion to the use of chemical weapons had been eroded in Douma and Salisbury.
"Bombing can not substitute for diplomacy", he said.
"Our service personnel have played an important role in terms of degrading the ability of the Syrian regime to use chemical weapons in the future", Williamson said.