The Pentagon said 59 Tomahawk missiles hit at 3:45am on Friday morning Shayrat airfield in Homs province, from where they believe the Syrian jets that dropped the chemicals on a rebel-held town in Idlib province had taken off.
Syrian state TV also reported a US missile attack on a number of military targets, calling it an "act of aggression."
The strikes, launched from two warships in the Mediterranean Sea, targeted the base's airstrips, hangars, control tower and ammunition areas, officials said.
It was the first direct military action the US has taken against Syrian President Bashar al-Assad's forces in the six-year war.
Syria's opposition National Coalition hailed the US strike, saying it puts an end to an age of "impunity" and should be just the beginning.
The US said initial indications were that the missiles had severely damaged or destroyed Syrian aircraft and support infrastructure and equipment at the airfield.
At least 86 people, including 27 children, were killed after a suspected poison gas attack on the rebel-held town of Khan Sheikhoun in Idlib province on Tuesday, according to the UK-based Syrian Observatory for Human Rights.
The attack drew widespread international condemnation and public revulsion, prompting the United Nations to pledge it would investigate it as a possible war crime.
The Syrian govenment denied carrying out the raid. Russia, a key military ally of the Assad government, has blamed the opposition, saying a government shell hit a building where rebels were producing chemical weapons. The rebels deny this.
"There can be no dispute that Syria used banned chemical weapons, violated its obligations under the chemical weapons convention and ignored the urging of the UN Security Council," Trump said.
The Pentagon said that Russia, which has been bombing rebel-held areas in Syria since 2015, had been notified ahead of the operation - but US Secretary of State Rex Tillerson said that Washington had "sought no approval from Moscow".
Earlier on Thursday, Russia's deputy ambassador to the United Nations warned of "negative consequences" if the US took military action against Syria.
"All responsibility, if military action occurred, will be on shoulders of those who initiated such doubtful and tragic enterprise," Vladimir Soronkov told reporters in response to questions about possible US strikes.
Turkey said samples from victims of the attack indicate they were exposed to sarin , a highly toxic nerve agent.
"I think what happened in Syria is a disgrace to humanity and he [President Bashar al-Assad] is there, and I guess he's running things, so something should happen," Trump had told reporters earlier on Thursday.
Christopher Swift, professor of national security studies at Georgetown University, said the most important question was whether the Trump administration's vision in launching the strikes was "an impulsive one or a strategic one".
It's not clear to me, yet, whether this administration has thought through the implications of the actions they took this evening," he told Al Jazeera.
"If the president has a plan, then it will be interesting to see how that plan comes through. But if he doesn't, he may have done more harm than good."
At the time of the US raid, Trump was at his Mar-a-Lago estate in Palm Beach, Florida, where he is holding two days of meetings with Chinese President Xi Jinping.
Trump said the strike on Syria was in the "vital national security interest" of the US.
Al Jazeera's James Bays, reporting Palm Beach, said: "This may be a one-off operation, but it will be quite difficult from now for Trump to get himself out of the argument over the future of Syria, the political future of Assad, the UN talks process in Geneva - the Trump administration is now at the centre of it all."
Syria maintains it did not use chemical weapons, blaming opposition fighters for stockpiling the chemicals.
"I stress, once again, that the Syrian Arab Army did not and will not use such weapons even against the terrorists who are targeting our people," Syria's Foreign Minister Walid Muallem told reporters in Damascus on Thursday.