Sonthi Boonyaratglin, the army's commander-in-chief launched the coup while Thaksin was in New York to attend a meeting of the United Nations general assembly on Tuesday.
Speaking on national television behalf of the rebels, Major General Prapas Sakuntanak said: "In order to maintain law and order, the Council for Political Reform has declared, first, that the Constitution of 1997 has been terminated."
"Second, the parliament - both the House of Representatives and the Senate - as well as the cabinet, have been terminated along with the Constitutional Court."
"We ask for the cooperation of the public and ask your pardon for the inconvenience"
Thai military statement
An army spokesman Colonel Akara Chitroj also told reporters that Chitchai Wannasathit, the deputy prime minister and a close ally of Thakshin's, had been removed from his post.
The military also imposed martial law on the capital and ordered all soldiers to report to their commanders.
Dozens of soldiers had earlier entered the Government House building and ordered police to put down their arms.
No casualties have been reported in the military takeover.
Thai PM at UN meeting
The military launches its coup as the country's democratically-elected leader, Thaksin Shinawatra, the prime minister, was attending a United Nations summit in New York.
Thaksin, who has cancelled his planned speech to the UN, has ordered troops not to move around the country illegally.
A government spokesman, Surapong Suebwonglee, also at the UN summit, said: "Some of the military officials came out and tried to make a coup attempt but we confirmed they cannot succeed."
The coup leaders made a
televised address to the nation
"Now we're in control," he said, adding it had not been decided when Thaksin would return home.
He has brought foward his address to the UN meeting from Wednesday and is now set to speak on Tuesday evening.
Tanks in streets
Despite the statements issued by Thaksin's aides in New York, the Thai army appears to be full control of the country.
News agencies in Bangkok, the Thai capital, have reported that numerous tanks and heavily armed troops have been deployed by the army around the centre of town and at key road intersections.
A spokesman for the military said on national television that the army was in full control of Thailand: "The armed forces commander and the national police commander have successfully taken over Bangkok and the surrounding area in order to maintain peace and order."
"There has been no struggle. We ask for the cooperation of the public and ask your pardon for the inconvenience."
Crisis building for months
Thaksin, who is attending a United Nations general assembly meeting in New York, has recently been under intense pressure to resign.
Protests earlier this year forced him to dissolve parliament and call a snap election for April.
The poll was boycotted by the opposition and the result was annulled by the court leaving Thailand without a working government.
New elections were planned for October 15 but have been postponed, probably until November.
Thailand's last military coup was 15 years ago.