The military does not execute its own condemned criminals - they are transferred (as are most long-term military prisoners) to the custody of the Federal Bureau of Prisons. The only Federal execution site at present is the high-security penitentiary at Terre Haute, IN, where Timothy McVeigh was executed a few years ago. This guy will almost certainly end up on Death Row there, and be executed there as a federal prisoner.
Unfortunately, execution is probably more to his taste than imprisonment. He'll be regarded as a martyr for Islam, and treated like a hero in most of the Islamic fundamentalist circuit. IMHO, better to sentence him to life imprisonment without parole, to avoid this.