The UK and France joined US action overnight with three waves of strikes beginning around 2am BST.
Speaking in Downing Street today the Prime Minister said strikes were “limited and targeted” and should be a “warning to Russia” before holding Bahar Assad’s regime accountable for the chemical attack.
Mrs May said last Saturday’s attack that killed as many as 70 people had caused “harrowing” scenes of innocent civilians foaming at the mouth.
The Prime Minister defended her decision not to give MPs a vote on the action and said she would speak to parliament on the matter on Monday.
Labour leader Jeremy Corbyn said the military action against Syria was “legally questionable” and makes real accountability for war crimes less likely.
Mrs May has faced criticism from across the political spectrum for failing to recall Parliament and put the plans to a vote.
The Prime Minister said she will go before the Commons on Monday to answer questions about her decision but insisted there was no “alternative path”.
She said all the indications were that it was a chemical weapons attack and the Government was “clear” Bashar Assad’s regime was responsible.
She said open source material showed barrel bombs had been used and a regime helicopter had been seen over the city on April 7.
Mrs May emphasised that none of the opposition forces used helicopters or barrel bombs, and that Daesh (Islamic State) does not have a presence in the region.
She said that the purpose of the strike was to “degrade and deter” the Syrian regime in its use of chemical weapons.
The Prime Minister cited similar attacks by the regime against its own people in June last year where 100 people were killed and more than 500 people became seriously ill.
The PM added: “No other group could have carried out this attack.”
Mrs May described the Assad regime’s use of chemical weapons as a “persistent pattern of behaviour”, adding that the British Government “judged it highly likely that the Syrian regime has continued to used chemical weapons since (the attack last June), and this must be stopped.”
She said the targets of the overnight attack included a chemical weapons store and a research centre used for the development of chemical weapons.
Referring to the Salisbury nerve agent attack, the Prime Minister also said that the military action “sends a clear message” to any country which uses such weapons.
Grilled on whether or not she believed it was right to support US strikes without allowing MPs a vote, the Prime Minister said she would be addressing parliament on Monday.
She said: said: “There is no graver decision for a prime minister than to commit our forces to combat and this is the first time I have had to do so.
“As always, they have served our country with the greatest professionalism and bravery, and we owe them a huge debt of gratitude.
“We would have preferred an alternative path but on this occasion there was none.
“We cannot allow the use of chemical weapons to become normalised, either in Syria, on the streets of the UK or elsewhere.
“We must reinstate the global consensus that chemical weapons cannot be used. This action is absolutely in Britain’s national interest.
“The lesson of history is when the global rules and standards that keep us safe come under threat we must take a stand and defend them.
“That is what our country has always done and that is what we will continue to do.”
Asked if the strikes had also been a warning to Russia, Mrs May said: “The action that took place last night was an action which was focused on degrading and deterring the operational capability and the willingness of the Syrian regime to continue to use chemical weapons.
“There have been many instances when we have seen them using those chemical weapons.
“But I believe it should also be a message to others that the international community is not going to stand by and allow chemical weapons to be used with impunity.”
Mrs May said chemical weapons had “all too often” been used in recent times.
“I think it is right that the international community has come together and said we will not accept this,” the PM added.
Additional reporting by Press Association.