The attacks early on Saturday came in response to a suspected chemical weapons attack in the former rebel stronghold of Douma last weekend.
"I ordered the United States armed forces to launch precision strikes on targets associated with the chemical weapon capabilities of Syrian dictator Bashar al-Assad," Trump said from the White House late on Friday.
Later, the US president tweeted saying the strikes were "Mission Accomplished!"
Targets were struck in Damascus, Homs and elsewhere in Syria, as Trump spoke.
A US official said the attacks were aimed at multiple sites and involved Tomahawk cruise missiles and fighter jets.
Confirming Britain's involvement in the attack, UK Prime Minister Theresa May said: "We would have preferred an alternative path. But on this occasion there is none."
She said the attacks were not about "regime change" or "intervening in a civil war", but were to "deter the use of chemical weapons" by the Syrian government.
French President Emmanuel Macron also confirmed France's involvement in the attack.
The purpose of the campaign is to "establish a strong deterrent against the production, spread and use of chemical weapons," Trump said.
Syrian state TV said that air defences responded to the attack by shooting down dozens of missiles. A Russian official said that 71 of a total of 103 missiles were downed by Syria's air defences.
But the Pentagon denied the missiles were deflected by Syrian air defences. "None of our aircraft or missiles involved in this operation were successfully engaged by Syrian air defences," Lieutenant-General Kenneth McKenzie, the director of the Joint Staff at the Pentagon, said.
In a press briefing on Saturday, the Pentagon said they believed the air strikes "attacked the heart of the Syrian chemical weapons programme".
President Bashar al-Assad told his Iranian counterpart Hassan Rouhani that the attack would increase Syria's resolve to "fight and crush terrorism in every inch" of the country, the Syrian presidency said on Saturday.
Condemning the attacks as a breach of international law, state news agency SANA said the attacks had also targeted army depots in the Homs area.
"The tripartite aggression is a flagrant violation of international law," SANA reported.
The Syrian presidency posted a video that appeared to show President Assad arriving for work on Saturday morning, hours after the attacks.
"The morning of resilience," declared the caption accompanying the video circulated on the presidency's Telegram feed.
The video showed Assad in a suit and tie and carrying a briefcase as he walked into the marble-floored entrance of his work palace in Damascus.
|Anatoly Antonov, Russia's ambassador to the US [File photo: Justin Sullivan/Getty Images]|
'Not without consequences'
Russia's ambassador to the US warned that there would be consequences for the attacks, adding that it was not acceptable to insult Russia's president.
"A pre-designed scenario is being implemented," Russian Ambassador Anatoly Antonov said on Twitter.
"Again, we are being threatened. We warned that such actions will not be left without consequences.
"Insulting the President of Russia is unacceptable and inadmissible," he added.
"The US - the possessor of the biggest arsenal of chemical weapons - has no moral right to blame other countries."
Russian defence ministry said that no US or allied missiles had entered Russian air defence zones in Syria.
Iran also warned of "regional consequences" following the attacks.
"The United States and its allies have no proof and, without even waiting for the Organisation for the Prohibition of Chemical Weapons to take a position, have carried out this military attack ... and are responsible for the regional consequences," said foreign ministry spokesman Bahram Ghasemi on his Telegram channel.
A senior official in a regional alliance that backs Damascus said the Syrian government absorbed the attacks, adding that the targeted sites were evacuated days ago thanks to a warning from Russia.
"We had an early warning of the strike from the Russians ... and all military bases were evacuated a few days ago," the official said.
"We are carrying out an assessment of the material damages," the official added.
The head of NATO expressed his support for the US-led attacks.
"I support the actions taken by the United States, the United Kingdom and France ... This will reduce the regime's ability to further attack the people of Syria with chemical weapons," Secretary-General Jens Stoltenberg said in a statement.
UN Secretary-General Antonio Guterres called for restraint and for countries to avoid any acts that could escalate the situation in Syria further.
Guterres delayed a planned trip to Saudi Arabia to deal with the aftermath of the military action.
"I urge all member states to show restraint in these dangerous circumstances and to avoid any acts that could escalate the situation and worsen the suffering of the Syrian people," Guterres said in a statement.
"Any use of chemical weapons is abhorrent. The suffering it causes is horrendous," Guterres said, adding it was important to act in line with the UN Charter and international law.
Al Jazeera's senior political analyst Marwan Bishara said despite the attacks, "the man responsible for this [Assad] remains at large and at the head of the Syrian regime."
"We more or less expected these attacks. There has been talks and a lot of boasting about the 'nice, smart' missiles and we've seen in the last 72 hours, the three allies getting together and looking at the evidence," he said.
US pivot to attacks
Only 10 days ago, Trump told national security aides that he wanted US forces out of Syria in about six months.
The US president was adamant that it was time to bring them home after largely defeating the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group.
"Very soon, very soon, we're coming out," Trump said to a crowd in Richfield, Ohio, on March 30.
"We're going to get back to our country, where we belong, where we want to be," he said.
But with Saturday's attacks, Trump has abruptly deepened US involvement in Syria.
Aides told Reuters news agency that Trump's attitude changed when he was shown images of Syrians allegedly killed by the chemical weapons last Saturday.
The attacks come about a year after he first ordered air raids against Syrian targets to retaliate for an earlier use of the banned substances.