Ibrahim al-Qosi "is already in Khartoum since early this morning" after his arrival on a US military aircraft, foreign ministry spokesperson Al-Obeid Meruh said.
"He is a free man," Meruh said.
Court documents in August 2010 showed that Qosi's 14-year sentence would be suspended this month and that he would be returned to Sudan.
He was the first Guantanamo detainee to be tried by military tribunal under revised rules introduced by the administration of President Barack Obama.
Under a plea deal, Qosi (50) admitted in July 2010 to providing support to terrorism and conspiracy. Details of the plea deal were not released at the time.
He had been held at the US-run Guantanamo prison since 2002.
Qosi acknowledged under oath that he had backed al-Qaeda since 1996 and had followed bin Laden to Afghanistan, where he worked as a cook at a compound in Jalalabad and also served as a bookkeeper and logistics chief.
Bin Laden, the world's most wanted man, was killed in a US raid on his Pakistan hideout in May last year.
Meruh said there had been "some sort of communication between American authorities and Sudanese authorities" over the Qosi case, and a team from the US visited Sudan last month to finalise details.
"They said they are going to release him," Meruh said.
Bin Laden lived in Sudan for about five years until he was forced to leave in 1996.
The US imposed sanctions on Sudan in 1997, partly for its support of international terrorism. – Sapa-AFP