"I'm ecstatic to get back home to my wife and the life that I had, helping chemically-dependent homeless vets," Weemer told reporters after the verdict.
"I have a lot of pride and honour in the Marine Corps."
The court martial marked the government's second loss in its case against members of the squad.
Captain Nicholas Gannon, the prosecutor at the court martial, called Weemer's defence argument "preposterous", saying that the soldier had made no reference to a struggle in interviews with the Secret Service and Naval Criminal Investigative Service.
In his closing argument on Wednesday Gannon said the captives should have been ordered outside to the street instead of being shot, and that Weemer had failed to follow his training on rules of engagement.
"I can't bring you an autopsy report," he said. "I don't have one, but we have a lot of evidence that shows you beyond a reasonable doubt that the accused shot an individual in the chest twice... The killing was unlawful."
The case came to light in 2006 when Weemer told a US Secret Service agent during a job interview that he had been involved in an unlawful killing in Iraq.
The admission prompted an investigation that led to charges against three marines - Weemer, Jose Nazario, the squad leader, and Sergeant Jermaine Nelson.
Nazario, who had left the Marine Corps by the time charges were brought, was cleared by a civilian jury last year. Nelson is awaiting a court martial.
During the one-week court martial, the defence argued that the government could not prove Weemer was guilty of murder because there were no bodies, no relatives complaining of a lost loved one and no forensic evidence.
Paul Hackett, the defence lawyer, told the jury of officers that Weemer had been "manipulated" during the interview in which he confessed and that the death occurred during the "fog of war".
"My interpretation was that they appreciated the chaos and kinetics of the environment," Hackett told reporters.
"In real simple terms, they believed Sergeant Weemer was justified in shooting in self-defence."