The strikes, in collaboration with the USA and France, are in response to an alleged chemical attack on the Syrian town of Douma last week.
But May said intelligence pointed to the Syrian government being behind the suspected chemical attack on the rebel-held Damascus suburb of Douma last Saturday, and Defence Secretary Gavin Williamson said speed was "essential".
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.
Corbyn, a veteran anti-war campaigner, said he had written to May to ask her to publish in full the legal advice she had received prior to taking action.
In a briefing at Downing Street on Saturday morning, May said she would have preferred an alternative path, instead of punitive strikes but that there was none available.
"It is about a limited and targeted strike that does not further escalate tensions in the region and that does everything possible to prevent civilian casualties".
May said the strikes would "also send a clear signal to anyone else who believes they can use chemical weapons with impunity".
"I think it is right that the global community has come together and said we will not accept this", she added.
Four RAF Tornados fired Storm Shadow missiles at a former missile base near Homs, following late-night talks between Theresa May, Emmanuel Macron and Donald Trump.
She said: "No other group but Syria's military could have carried out the chemical attack". "We can not allow the use of chemical weapons to become normalized - within Syria, on the streets of the United Kingdom, or anywhere else in our world".
The Syrian Regime has a history of using chemical weapons against its own people in the most cruel and abhorrent way.
This persistent pattern of behavior must be stopped - not just to protect innocent people in Syria from the horrific deaths and casualties caused by chemical weapons but also because we can not allow the erosion of the global norm that prevents the use of these weapons.
Iranian President Rouhani says US-led military strikes in Syria will cause "destruction" in the Middle East.
"As we have seen in the past, inaction has its consequences - so PM right to join forces with our allies to take targeted & appropriate action". We have sought to use every possible diplomatic channel to achieve this.
Mrs May said chemical weapons had "all too often" been used in recent times.