Sosa, who was arrested in Canada in 2011, where he also holds citizenship, and extradited to the U.S., was convicted by a jury in 2012 of making false statements and illegally obtaining citizenship in 2007.
Sosa, a former second lieutenant in the Guatemalan army, was accused by comrades of firing a gun into a well filled with screaming villagers, and of doing nothing as soldiers in his command raped and killed women. At least 160 people were killed in the Guatemalan village on the date.
Sosa said he did not receive a fair trial. He said he was not in the village at the time and plans to appeal.
"I did not have a just trial and ... the truth was covered," Sosa said in Spanish through a court interpreter. "I am innocent and I am not guilty."
"These are the crimes the defendant lied about and didn't disclose," U.S. District Court Judge Virginia Phillips told the court before handing down the maximum 10-year sentence. "The particular facts of what occurred on Dec. 7, 1982, at Dos Erres cannot be characterized in any other way than as crimes."
Sosa could be returned to Guatemala after serving his sentence, according to the U.S. Department of Justice. Guatemala is seeking his extradition to prosecute him for the massacre.
The case is one of several aimed at perpetrators of the massacre that took place at the height of Guatemala's 36-year civil war. In that nation, five former soldiers have each been sentenced to more than 6,000 years in prison for the killings, while one of Sosa's former comrades is also serving a decade-long sentence in a U.S. prison for lying on his immigration forms.
At least 200,000 people were killed during the civil war in Guatemala, mostly by state forces and paramilitary groups seeking to wipe out a left-wing uprising. The U.S. supported Guatemala's military governments during the war.
After the war, Guatemala issued arrest warrants for more than a dozen soldiers implicated in the killings, but the cases languished until the Inter-American Court of Human Rights in 2009 demanded the country prosecute the perpetrators.
The Associated Press contributed to this report.