Thailand's revered king has given his backing to coup leader Gen Sonthi Boonyaratglin, state-run TV says.
Families took pictures in front of the tanks on Bangkok's streets
King Bhumibol Adulyadej has not spoken in person, but a statement attributed to him said he appointed Gen Sonthi as head of a new executive body.
The ousted Prime Minister Thaksin Shinawatra - who was in New York at the time of the coup - is now in London.
Gen Sonthi says a new prime minister will be named within two weeks. The US has urged a swift return to democracy.
Gen Sonthi said elections would be held within a year, after a new constitution had been drafted.
The coup leader is said to be close to the king, although he says the monarch had nothing to do with the coup.
The television statement said King Bhumibol urged all Thais to "remain peaceful" and called for civil servants to listen to orders from Gen Sonthi.
The BBC's Jonathan Head in Bangkok says securing the endorsement of the 78-year-old monarch is crucial to the success of the military intervention.
White House press secretary Tony Snow said the US was "disappointed" in the coup and said talks on a US free trade agreement with Thailand depended on a swift return to democracy.
But the BBC's Jonathan Beale says Washington has not given any messages of support for Mr Thaksin, suggesting that the US is trying to avoid taking sides.
The coup followed months of growing tension in Thailand, with protests against Mr Thaksin and a general election which was annulled due to concerns about its legitimacy.
Many in Bangkok, where Mr Thaksin is unpopular, welcomed the news.
During the day, coup supporters brought flowers, pizzas and donuts to the soldiers and took turns taking family pictures in front of the armoured vehicles which have cordoned off the government district.
Many of the tanks that have been deployed in Bangkok have yellow ribbons tied around their barrels to signify loyalty to the king.
Gen Sonthi says he was acting in line with the wishes of the Thai people, blaming government mismanagement for forcing coup leaders to act.
He said coup leaders were considering candidates to appoint as the new prime minister.
A new national assembly would be appointed to draft a new, permanent constitution, under which elections would be held within a year, he said.
The deposed prime minister arrived in the British capital with little fanfare, on what the British Foreign Office says is a private visit.
He smiled and waved as he got off the plane, but did not address the press. He is thought to be planning to visit family members.
Thailand's regional neighbours expressed shock and concern at the events.
It is the first coup attempt in 15 years in a country where they used to be commonplace. There were 17 of them between 1932 and 1991.