The soldier had been charged with premeditated murder and had pleaded not guilty, the source said.
The incident in November had led to tensions between Washington and its Middle Eastern ally.
Jordanian authorities at first said the U.S. trainers had been shot dead by the soldier when their car failed to stop at the gate of the base. Washington rejected that account and said it could not rule out a political motive for the killings.
Jordan hosts several hundred U.S. contractors in a military cooperation programme which includes the stationing of U.S. F-16 fighter jets. They use Jordanian airfields to hit ‘Daesh’ positions in neighboring Syria and to protect its borders.