"There was absolutely no apology or remorse or repentance in the man's eyes," he told Sky News.
"(When) our people took him to the gallows room he wondered what was going on, he looked dazed, (as though) not believing what was going to happen.
"I looked at him and he kept staring at me, and he said 'Don't be afraid, this is the way we will go'.
"He was offered a hood, but he turned it down. He said 'There's no need for that'.
"It was so quick, and totally painless."
Mr al Rubaie had earlier told state-run Iraqiya television: "He did not ask for anything. He was carrying a Koran and said: 'I want this Koran to be given to this person,' a man he called Bander," adding he did not know who Bander was.
"Saddam was treated with respect when he was alive and after his death," he added. "Saddam's execution was 100 percent Iraqi and the American side did not interfere."
Sami al-Askari, political adviser to Prime Minister Nouri al Maliki, said Saddam struggled when he was taken from his cell in an American military prison, but was composed in his last moments.
He said Saddam was clad completely in black, with a jacket, trousers, hat and shoes, rather than prison garb.
Shortly before the execution, Saddam's hat was removed and Saddam was asked if he wanted to say something, but Mr al Askari said he had not wanted to, though he did recite a Muslim prayer.
"Before the rope was put around his neck, Saddam shouted: 'God is great. The nation will be victorious and Palestine is Arab'."
It has not been revealed where the execution took place, but it is believed it was not held in the fortified Green Zone.
One official said it took place at a facility known to Americans as 'Camp Justice', a former base for Saddam's feared security services and now used regularly for executions by Iraqi's courts.