He was later sentenced to 15 years in prison for illegally crossing the border from Syria.
The Iraqi government said at the time of his arrest that Sabawi and his brothers had been "providing financial support, weapons and explosives." to anti-US armed groups.
Ayman's father was captured in February last year.
Ayman had been head of the intelligence service under Saddam, and was number 36 on a US list of the 55 most-wanted members of the former government.
The elder Sabawi testified on behalf of Saddam during his trial over the execution of 148 Shia Muslims from the town of Dujail where there had been an assassination attempt against the former leader.
Saddam was condemned to death last month but has appealed against the verdict.