The barrage that killed two officers was driven by religious extremism, prosecutors in Fort Bragg, North Carolina, said on Thursday.
Sergeant Hasan Akbar, who gave a brief, barely audible apology hours earlier, stood at attention between his lawyers as the verdict was delivered. He showed no emotion.
He could have been sentenced to life in prison with or without parole for the early morning March 2003 attack, which also wounded 14 fellow members of the US Army's 101st Airborne Division at Camp Pennsylvania in Kuwait.
The 15-person military jury, which last week took just two and a half hours to convict Akbar of premeditated murder and attempted premeditated murder, deliberated for about seven hours in the sentencing phase.
After jurors reached a verdict, they voted on whether to reconsider the decision after one juror asked that they do so.
The sentence will be automatically appealed. If Akbar is executed, it would be by lethal injection.
Kuwait served as a launchpad
for the US-led invasion of Iraq
"I want to apologise for the attack that occurred. I felt that my life was in jeopardy, and I had no other options. I also want to ask you for forgiveness," Akbar told the jury before it deliberated in the sentencing phase.
Akbar, 34, spoke for less than a minute, delivering an unsworn statement that could not be cross-examined. He spoke in such a low voice that even prosecutors sitting nearby had trouble hearing, with one lawyer even cupping his ear.
While the defence contends Akbar was too mentally ill to plan the attack, they have never disputed that he threw grenades into troop tents in the early morning darkness and then fired on soldiers in the ensuing chaos.
Army Captain Chris Seifert, 27, and Air Force Major Gregory Stone, 40, were killed.
Prosecutors say Akbar launched the attack at his camp - days before the soldiers were to move into Iraq - because he was concerned about US troops killing fellow Muslims in the Iraq war.
"He is a hate-filled, ideologically driven murderer," chief prosecutor Lieutenant-Colonel Michael Mulligan said.
"He is a hate-filled, ideologically driven murderer"
He added that Akbar had written in his diary in 1997: "My life will not be complete unless America is destroyed."
Akbar is the first American since the Vietnam era to be prosecuted on charges of murdering a fellow soldier during wartime.
Defence attorney Major David Coombs told jurors that a sentence of life without parole would allow Akbar to be treated for mental illness and possibly rehabilitated.
"Death is an absolute punishment, a punishment of last resort," Coombs said.
A defence psychiatrist testified that although Akbar was legally sane and understood the consequences of his attack, he suffered from forms of paranoia and schizophrenia.
If given a death sentence, Akbar would join five others on the military's death row at Fort Leavenworth, Kansas. The last US military execution was in 1961.