The murder of Kassim Hassan took place when US soldiers spotted a garbage truck apparently dropping homemade bombs in Sadr City, the capital's most populous Shiite Muslim neighbourhood.
The soldiers started shooting at the truck, which caught fire, and Horne said he pulled a severely wounded Hassan out of the burning truck.
"About seven or eight minutes later, he fell to the ground," said 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.
"I wanted to end his suffering," Horne said. "It was my opinion that he could not be helped."
Horne was also found guilty of conspiracy with two other soldiers, Staff Sergeant Cardenas Alban and Second Lieutenant Erick Anderson, to commit murder. They have yet to stand trial.
Horne said that after seeing Hassan lying on the ground, he contacted Alban and Anderson.
Anderson "asked what I needed and I took him to see the victim. His response was 'Holy Christ, what do you want to do?'"
"I can't leave him, I want to put him out of his misery. Anderson said 'So do it.'"
Horne said that he shone a flashlight on Hassan, and quoted Alban as saying: "My God, he's just a kid, he's not going to survive."
Horne said he then heard a burst of gunfire from Alban.
"I could hear gurgling sounds, attempts to breathe. I took a few steps back and fired one round ... I hit him in the back of the head. There were no signs of life."
Anderson "agreed it needed to be done," said Horne, adding that when he consulted his superior officer on the wounded Iraqi it was "like a sanity check, to make sure we were both thinking in the same terms. We both had the assumption that he was suffering and wasn't going to survive."
Sergeant Jacob Smith, also on the operation, said there was nothing to be done for Hassan.
"Everywhere from his ribs to his hip was a hole ... you could see his intestines and spinal cord ... it looked like his skin had just melted off ... everything pretty much fell out of his stomach."
Horne was found not guilty on another charge of solicitation to commit premeditated murder.
He was originally charged with premeditated murder, but pleaded guilty to the lesser charge as part of the pre-trial agreement.
A forensic psychiatrist who interviewed Horne said that he had "lost his sense of professional distance from victims ... he showed signs of being emotionally overwhelmed ... there is no indication he is prone to violence".
A 10-member panel of Horne's fellow soldiers expected to agree a sentence on Saturday was reduced to seven after three were requested to be removed by defence attorney, First Lieutenant Stanley Martin, and prosecutor Captain John Maloney.