Staff Sergeant Johnny Horne on Friday was convicted of the unpremeditated murder of a severely wounded Iraqi civilian in Baghdad's Sadr City district on 18 August.
A pre-trial agreement limits sentencing to 10 years, without which the charge carried a maximum sentence of life imprisonment.
The murder of Qasim Hasan took place when US soldiers spotted a garbage truck apparently dropping homemade bombs in Sadr City.
The soldiers started shooting at the truck, which caught fire, and a severely wounded Hasan pulled himself out of the truck and fell to the ground, according to previous testimony.
"I wanted to end his suffering; it was my opinion that he could not be helped"
US Staff Sergeant Johnny Horne
"When I found him, I came to the conclusion that he needed to be put out of his misery," Horne said. "I fired a shot into his head and his attempts to breathe ceased."
Judge Colonel Stephanie Browne asked Horne what his intention was when he fired the shot, to which Horne replied: "I wanted to end his suffering; it was my opinion that he could not be helped."
Horne was also found guilty of conspiracy to commit murder with two other soldiers, Staff Sergeant Cardenas Alban and Second Lieutenant Erick Anderson, who have yet to stand trial.
In a separate development, Turkish Prime Minister Recep Tayyip Erdogan has warned US troops in Iraq to take care not to kill civilians.
Erdogan conveyed Turkish
concerns to US administration
"There are people in Iraq who believe in defending their country. These are people we call resistance fighters," he said.
"Can we see those who resist in the same light as we see terrorists?" Erdogan was quoted by the Anatolia news agency as telling Turkey's Kanal D television channel in an interview from Brussels late on Thursday.
"Can we approve the killing of defenceless women and children under a hail of bombs?" he added.
Citing TV footage of a US marine gunning down what appeared to be a wounded, unarmed Iraqi in a mosque in Falluja, Erdogan said he had conveyed Ankara's concerns over the US assault against the city to US Vice-President Dick Cheney.
"The killing of defenceless people in places of worship in Falluja leads to outrage and hurts us. These [acts] are not right," the Turkish leader said.
"The killing of defenceless people in places of worship in Falluja leads to outrage and hurts us"
Recep Tayip Erdogan,
Turkish prime minister
Erdogan denied, however, that there was any tension over the issue between Ankara and Washington.
The Turkish parliament, dominated by Erdogan's Justice and Development Party, in 2003 voted against allowing the US to use Turkish territory to open a northern front in Iraq.
Public opinion surveys regularly show that an overwhelming majority of Turks is opposed to the US presence in Iraq, Turkey's southern neighbour.