Mr Trump thanked the UK and France “for their wisdom and the power of their fine military” in his first tweet since the US, UK and France launched missiles against Syria on Saturday.
He wrote: “A perfectly executed strike last night. Thank you to France and the United Kingdom for their wisdom and the power of their fine Military. Could not have had a better result. Mission Accomplished!”
The president also hailed the his country’s “great military”, which he said “will soon be the finest our country has ever had”, in the second of two tweets on Saturday.
He added: “So proud of our great Military which will soon be, after the spending of billions of fully approved dollars, the finest that our Country has ever had. There won’t be anything, or anyone, even close!”
It comes after the three nations launched strikes at three sites connected to the Syrian regime’s chemical weapons programme.
The action was launched in retaliation to the purported chemical attack in Syria that the Government has said was “clearly” carried out by Syrian President Bashar al-Assad’s regime.
Prime Minister Theresa May said on Saturday the strikes were “limited and targeted”, adding that they were “successful”.
Syria and main backer Russia said more than 100 missiles had been fired while footage from Syrian state TV appeared to show huge craters following the blasts.
Mr Trump had earlier said that Syria’s use of chemical weapons was a “significant escalation in a pattern of chemical weapons use by that very terrible regime”.
Giving a statement at the White House, the president said: “This evil and despicable act left mothers and fathers and children thrashing in pain and gasping for air.
“The combined American, British and French response will integrate all instruments of our national power.”
Russian leader Vladimir Putin condemned the strikes as an “act of aggression” and threatened “consequences for the allies”.
He called an emergency meeting of the UN security council, which will be held at 4pm BST today.
Syrian military claimed three civilians were injured, while most of the missiles launched were shot down, it said.