The soldier, Marik al-Tuwayha, had opened fire on the trainers in November as their vehicle approached al-Jafr airbase in November. He claimed that he had friendly relations with the US soldiers, and no reason to kill them.
Witnesses to the November 4 incident said that a four-car convoy was entering the base when Jordanian guards heard a low sound and thought it might be a pistol shot.
"Despite this tragedy, Jordan remains a strategic partner", Barbee added.
Relatives of the victims, who have described video of the scene, said the footage shows that Tuwayha was shooting for six minutes and did not stop even when the Americans identified themselves as allies.
Jordan is a close ally of the United States and has been participating in coalition airstrikes purportedly against the Daesh Takfiri terrorist group in Iraq and Syria.
"We are reassured to see the perpetrator brought to justice", the U.S. Embassy in Jordan said in a statement.
In Jordan, life in prison can mean 20 years, with time off for good behavior.
Charles Lewellen, 53, whose son was killed, later told The Associated Press that the verdict "won't take the pain away", but that it proved "what we have been saying all along.that he murdered our sons". He said the USA respects Jordan's military process and praised Jordan for adhering to its own laws in resolving the case expeditiously.
Sergeant Tawayha said at his trial that he did not resent the American presence at the base.
The video was shown to the family by US law enforcement, but has not been released to the public. It said that all three had been following "established procedures for entering the gate".
A Jordanian military court also made a decision to expel the soldier - whose identity was not announced - from the armed forces and fine him for the value of the 70 bullets he fired at the Americans' vehicle, Efe news reported.
Cynthia Lewellen, 53, the mother of Matthew Lewellen, expressed sympathy for all those affected by the shooting, including the family of the defendant.
Jordan had initially suggested that the USA troops had triggered the shooting by entering the gate with improper procedures, a claim refuted by the US and later withdrawn.