The defendant, 1st Sgt. Marik al-Tuwayha, had pleaded "not guilty", saying he opened fire because he feared the base was coming under attack.
The U.S. soldiers killed were Staff Sgt. James Moriarty, 27, of Kerrville, Texas; Staff Sgt. Kevin McEnroe, 30, of Tucson; and Staff Sgt. Matthew Lewellen, 27, of Kirksville, Mo. He insisted that he was protecting the base, which he thought was coming under attack.
"Despite this tragedy, Jordan remains a strategic partner", he 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 member of the US-led worldwide coalition that has been bombing positions of the Islamic State terror organisation in Syria and Iraq since 2014.
Eric Barbee, a spokesman for the United States Embassy in Amman, Jordan, which sent observers to the trial, said the proceedings "confirmed that the deceased US service members followed all established procedures when accessing the base the day of the incident".
The defendant, al-Tuwayha, as well as some other gate guards on duty that night, testified that they heard what might have been a gun shot coming from the direction of the United States convey.
He was sentenced to "hard labour for life", a term which lasts 20 years but could extend to life in jail, a judicial official told AFP.
Sergeant Tawayha said at his trial that he did not resent the American presence at the base.
Members of the families of the dead were present at the court but did not speak to the press. They yelled that they were friendly forces, the relatives said.
At the start of the trial, the military court Judge Colonel Mohammed al-Afeef said the defendant had no known ties to jihadist organizations.
In the letter, a copy of which was given to the AP, Moriarty listed several demands to Jordan.
"In this verdict, nobody comes out happy", she said.
Al-Tuwayha's defense lawyer intends to appeal the verdict.
Jordan has ruled out terrorism in the November shooting in which the convoy of the US Army Green Berets came under fire at the base entrance.