Pentagon officials said the missiles first struck a scientific research centre near Damascus that develops, produces and tests chemical and biological weapons.
The UN Secretary-General, Antonio Guterres, described the use of chemical weapons as "abhorrent", but stressed that member states must act in accordance with "international law in general". "This must be stopped".
President Donald Trump on Saturday praised the USA military, the United Kingdom, and France for the operation.
It was the second time in little over a year that the Trump administration has launched retaliatory strikes against Assad's army in the wake of chemical attacks.
Meanwhile, his British ally, Prime Minister Theresa May, has been captaining a sinking ship since the Brexit vote, and is keen to appear strong and decisive, especially since the suspected Russian nerve agent attack on defector Sergei Skripal in Salisbury last month. The use of chemical weapons is merely a small part of the regime strategy.
"We're not cooperating with them in Syria".
"Nobody should doubt British resolve", she added. There is nothing here that could possibly go wrong, I mean, there are no historical warnings about using military intervention when the evidence doesn't exist and only later it is revealed that the evidence they did claim was in fact, fabricated entirely.
"It was right to take the action that we have done in the timing that we have done", she said.
Following the attacks, hundreds of Syrians gathered at landmark squares in the Syrian capital, honking their auto horns, flashing victory signs and waving Syrian and Russian flags in scenes of defiance.
Russian Federation entered Syria's civil war in 2015 and has backed the Assad regime.
Syria state TV, however, claimed that three civilians were wounded in Homs after "several" missiles were intercepted by Syrian air-defense systems.
The Damascus sky lights up missile fire as the USA launches an attack on Syria targeting different parts of the capital early Saturday, April 14, 2018.
The French military has said it does not believe any of its missiles were intercepted.
Theresa May says air strikes in Syria should act as a warning to Russian Federation over its use of chemical weapons.
President Vladimir Putin has said Russian Federation will call an emergency session of the UN Security Council over air strikes on Syria.
German Chancellor Angela Merkel - who had ruled out joining the military action - said she supported the strikes as "necessary and appropriate". "The use of such weapons is inacceptable and should be prosecuted in every circumstances and anywhere they are used".
Explosions hit the capital, Damascus, as well as two locations near the city of Homs, the Pentagon said.
Putin's foreign ministry has branded the attacks a "tremendous blow to the negotiation process".
McKenzie said there were no initial reports of civilian casualties in large part because the operation was planned to be carried out during the night.
Iranian President Rouhani says US-led military strikes in Syria will cause "destruction" in the Middle East.
"Never said when an attack on Syria would take place".
Making the case for military action, the document further stated: "The UK is permitted under global law, on an exceptional basis, to take measures in order to alleviate overwhelming humanitarian suffering... there is convincing evidence, generally accepted by the worldwide community as a whole, of extreme humanitarian distress on a large scale, requiring immediate and urgent relief".