"He was executed today (Thursday)," AFP quoted Haidar al-Saadi as saying on Thursday.
"The Ministry of Justice implemented the execution sentence against the criminal [Mahmud]…for genocide," Saadi added.
Mahmud was Saddam’s personal secretary and chief bodyguard.
He was arrested on June 16, 2003 and eventually sentenced to death on October 26, 2010 on charges of orchestrating a crackdown against rival political parties in the country in the 1980s and 1990s. The suppressive campaign included assassinations and unlawful detentions.
He is the latest in a series of former senior regime officials to be executed by Iraq’s new rulers since the toppling of Saddam nine years ago. Saddam was executed by hanging in 2006.
The last execution of a former regime official took place in January 2010 when Saddam’s notorious cousin, known as “Chemical Ali” for his role in poison gas attacks, was put to death by hanging.
Saddam’s long-term Foreign Minister Tariq Aziz was also sentenced to death in 2010 and awaits execution.