Ibrahim al Qosi was sentenced to 14 years after pleading guilty in 2010 to conspiring with al Qaeda and providing material support to terrorism, the Pentagon said in a statement.
He completed his reduced, two-year sentence before his transfer took place, the statement said.
The Pentagon declined to say whether Qosi, described as a "cook and sometimes driver" for al Qaeda, had been freed in Sudan or held by the government there.
"We coordinated with the government of Sudan on appropriate security measures to mitigate any threat that he continues to pose," said Lieutenant Colonel Todd Breasseale, a Pentagon spokesman.
Qosi was alleged to have run the kitchen at bin Laden's Star of Jihad compound in Jalalabad, Afghanistan, and of having been part of an al Qaeda mortar crew.
He was accused of acting as a cook and bodyguard for the former al Qaeda leader, who was killed by US forces in Pakistan last year, and helping him escape to the Tora Bora mountains of Afghanistan in 2001.
He was captured in Afghanistan in December 2001 and first charged in the Guantanamo court system known as military commissions in 2004.
US efforts to resettle prisoners cleared for release from Guantanamo Bay, set up in Cuba after the September 11, 2001, attacks, have been stymied by government refusals to allow any into the United States and by other restrictions imposed by Congress.
In April two members of China's Muslim Uighur minority became the first prisoners to leave Guantanamo Bay in more than 15 months. They were resettled in El Salvador.
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