Aziz, 79, served as foreign minister and deputy prime minister and was a close adviser to the former leader.
He was sentenced to death by the Iraqi Supreme Court in 2010 for the persecution of religious parties under Saddam's rule but was never executed.
He surrendered to US troops in 2003 shortly after the fall of Baghdad.
A local health official told reporters that he was taken to hospital from prison after suffering a heart attack. Initial reports said he had died in prison.
He had long been in poor health, suffering from heart and respiratory problems, high blood pressure and diabetes, and his family repeatedly called for his release from custody.
His wife, Violet, had visited him in prison on Thursday, their daughter Zeinab told the AP news agency.
She said her father had suffered several strokes that left him confined to a wheelchair and unable to speak during her parents' final meeting.
"He didn't move. He couldn't talk. He didn't say a word to her. He just looked at her," said Zeinab, adding: "It is so sad that he had to go this way."