Arid Uka, 21, allegedly approached a bus at the airport on March 2 and asked in English if it was carrying Americans before shooting dead the driver and a passenger and wounding two other US Air Force personnel.
"As Uka fired his gun, he repeated aloud an Arabic expression that means 'God is great,' and continued shooting until his gun did not fire," read a statement put out by federal prosecutors in New York.
The US complaint accused Uka of two counts of murder, one count of attempted murder, one count of using a firearm in a violent crime and a fifth count of committing a deadly act at an international civil airport.
Uka is currently detained in Germany, where he faces similar charges over what has been described as the first Islamic extremist attack on German soil.
German prosecutors believe Uka carried out the attack to avenge what he saw as atrocities by US troops in Afghanistan but have said they are not aware of links between him and terror groups.
The killings have had ramifications for American military personnel in Germany. Security was ramped up in their wake and soldiers were ordered not to wear their uniforms in public.
It was not immediately clear whether the charges filed in New York indicated that Uka could face trial in the United States.