The office of John Negroponte, the US national intelligence director, said in a statement on Monday: "Analysis of air samples collected on October 11, 2006, detected radioactive debris which confirms that North Korea conducted an underground nuclear explosion."
The statement provides the first official confirmation from the US that a nuclear detonation took place, as Pyongyang has claimed.
Negroponte's office also confirmed that the size of the explosion was less than 1 kiloton, a comparatively small nuclear explosion.
Each kiloton is equal to the force produced by 1,000 tonnes of TNT.
By comparison, the nuclear bomb the US dropped on Hiroshima, Japan, in 1945 was about 12.5 kilotons.
On Friday, a senior Bush administration official said that one test conducted on samples gathered after the detonation found a radioactive gas consistent with a nuclear explosion.
At the time, however, US intelligence was not ready to confirm that a nuclear test had actually taken place.