Theresa May said the UK is "confident" the "limited and targeted strikes" had degraded the Assad regime's ability to use chemical weapons.
Mrs May said it had been "right and legal" to take action.
Speaking in Downing Street, she said: "This collective action sends a clear message that the international community will not stand by and tolerate the use 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.
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Military bases near the capital Damascus and the city of Homs were targeted, after an alleged chemical attack on the Syrian town of Douma.
The Ministry of Defence said Storm Shadow missiles were launched by four RAF Tornados at a former missile base 15 miles west of Homs, where it is thought the Assad regime is stockpiling items used to make chemical weapons.
A spokesperson added the facility was "located some distance from any known concentrations of civilian habitation" and scientific analysis was used to "minimise any risks of contamination to the surrounding area".
The strikes have prompted a mixed reaction, including criticism that military action was ordered without a debate in Parliament.
Labour leader Jeremy Corbyn has called the strikes "legally questionable".