The four were taking part in the Cold Response military exercises involving30,000 troops from NATO and partner countries.
About 200 planes and some 50 ships are taking part in the exercises, which will continue until April 1.
Their plane, a V-22B Osprey aircraft belonging to the US Marine Corps, was reported missing on Friday evening south of Bodo in northern Norway.
At 01:30 (0030 GMT) on Saturday, “the police arrived at the scene.
The police in Nordland County now confirm that the crew of four have died.
As far as the police know, the four are of American nationality,” the Norwegian defence ministry said in a statement.
The US Marine Corps said in a statement that four Marines were listed as “duty status whereabouts unknown” following “an aviation incident” involving a MV-22B Osprey.
It said their identities would not be released until 24 hours after the soldiers’ next of kin had been notified.
“It’s with great sadness that we received the message saying that four American soldiers died in a plane crash last night,” Norwegian Prime Minister Jonas Gahr Store said on Twitter.
Cold Response 2022 aims to test how Norway would manage allied reinforcements on its soil in the event that NATO’s mutual defence clause were triggered.
Tensions between Russia and NATO have soared following Moscow’s invasion of Ukraine, but the exercises were planned long before that offensive began on February 24.