They said they had dissolved the constitution, suspended all institutions and closed the nation's borders.
Niger President Mohamed Bazoum has been held by troops from the presidential guard since early on Wednesday.
He was promised Washington's "unwavering support" in a call from US Secretary of State Antony Blinken.
UN Secretary General Antonio Guterres also said he had spoken to the president and offered the UN's full support.
Mr Bazoum is a key Western ally in the fight against Islamist militancy in West Africa.
Two neighbouring countries, Mali and Burkina Faso, have experienced coups triggered by jihadist uprisings in recent years.
In both countries the new military leaders have fallen out with France, the former colonial power, which also formerly ruled Niger.
In the TV announcement on Wednesday, Col Maj Amadou Abdramane, alongside nine other uniformed soldiers behind him, said: "We, the defence and security forces... have decided to put an end to the regime you know.
"This follows the continuing deterioration of the security situation, and poor economic and social governance."
He also said that all of the country's institutions had been suspended and that the heads of the ministries would take care of day-to-day business.
"All external partners are asked not to interfere," he went on. "Land and air borders are closed until the situation has stabilised."
He added a night curfew would take effect from 22:00 until 05:00 local time until further notice.
Col Maj Abdramane said the soldiers were acting for the National Council for the Safeguard of the Homeland (CNSP).
After the soldiers' TV announcement Mr Blinken called for the release of President Bazoum.
