NATO's Supreme Allied Commander Europe, US Army General Christopher Cavoli, briefed NATO allies about the incident, which was roundly condemned by the White House and the Pentagon - which warned of the risk of escalation.
Two Russian Su-27 jets carried out what the US military described as a reckless intercept of the US spy drone before one of them collided with it at 7.03am.
Several times before the collision, the Russian fighter jets dumped fuel on the MQ-9 - possibly trying to blind or damage it - and flew in front of the unmanned drone in unsafe manoeuvres, the US military said.
"Our MQ-9 aircraft was conducting routine operations in international airspace when it was intercepted and hit by a Russian aircraft, resulting in a crash and complete loss of the MQ-9," US Air Force General James Hecker, who oversees the US Air Force in the region, said in a statement.
"In fact, this unsafe and unprofessional act by the Russians nearly caused both aircraft to crash."
There was no immediate comment from Russia.
The US military said the incident followed a pattern of dangerous behaviour by Russian pilots operating near aircraft flown by the US and its allies, including over the Black Sea.
The Black Sea lies between Europe and Asia and is bordered by Russia and Ukraine, among other countries.
The White House said the drone's downing was unique, however, and would be raised directly with Russia.
"The State Department will be speaking directly with their Russian counterparts, and expressing our concerns over this unsafe and unprofessional intercept," White House National Security Council spokesman John Kirby said.
