Prosecutors said Green was the ringleader of a group of five soldiers who plotted to invade the home of the family of four to rape the girl.
They said he later bragged about the crime, saying what he had done was "awesome".
Green, 19 at the time of the crime, was described as the trigger-man in the group who donned black "ninja" outfits and raped Abeer Qassim Hamza al-Janabi and shot her, her father, mother and six-year-old sister.
"I do think it will allow him to have some semblance of a life and I'm very grateful for that"
Doug Green, brother of convicted soldier
The soldiers later set fire to the girl's body to try to cover up the crime.
The rape-murders took place after the soldiers drank whiskey, played cards, and plotted the attack in Mahmudiya, 30km south of the Iraqi capital, the court heard.
Three of the four other soldiers pleaded guilty in the attack and the fourth was convicted, all in military courts martial.
They were sentenced to between five and 100 years, but could be paroled much sooner.
Green was tried in federal court as a civilian on murder, rape and obstruction of justice charges because his arrest came after he was discharged from the army for a "personality disorder".
The defence team acknowledged that he took part in the killings but argued that he should be spared the death penalty.
During the trial Green was depicted as a victim of a bad childhood and combat stress after the death of close colleagues in the combat zone south of Baghdad.
"Steven Green was responsible [for the rape and murders] but the United States of America failed Steven Green," Scott Wendelsdorf, a defence lawyer, told the jury in his final submission.
"And it failed a lot of soldiers in Iraq. And that wouldn't amount to a hill of beans if it were not the United States of America now seeking to put Steven Green to death."
As representatives of the Iraqi family openly wept in court, Green smiled slightly when the jury gave its decision.
His father, John Green, said the result was "the better of two bad choices, but the better one by far".
The ex-soldier's brother, Doug, added that "it's the only appropriate verdict" given the choices.
"I have mixed emotions about it, but I do think it will allow him to have some semblance of a life and I'm very grateful for that.