All three men were sentenced for their role in the crackdown on Dujail, a mainly Shia town north of Baghdad, which followed a 1982 assassination attempt on Saddam Hussein.
There was more drastic repression against Shia following a 1991 uprising.
The death sentences have to be confirmed by the presidential council.
Aziz’s son, Ziad, who has lived in Jordan since 2003, called the verdict “an act of revenge”.
"The decision was an act of revenge against anybody and anything related to the past," he said, claiming that it proved the credibility of last week’s WikiLeaks revelations about the post-invasion Iraqi state.
"Like most of the trials carried out in Iraq, it does not meet international standards," comments journalist and author Ribert Fisk.
"Many people in Saddam's retinue did worse things than Tarek Aziz did. If anything he was a force of - if you can call it that - modration, but at least a restraint on some of the madder aspects of the regime."
Many in the Arab world will see the sentence as a sectarian move by the Shia-dominated authorities, Fisk believes, adding that Aziz was a potentially embarrassing witness to the West's complicity with the regime.
"Tarek was very close to the top of the regime and he would have known, especially when he was foreign minister, of the degree to which the West assisted the arming of Saddam Hussein in the early part of the Saddam regime, particularly from the United States of the components used by the Iraqis in gas shells and bombs which they got to use in Halabja.
"That's why they got rid of Saddam, for they did not want to get into the gas issue there. And that's why they're getting rid of Tarek Aziz."
Who is Tareq Aziz?
Tareq Aziz was appointed Iraqi information minister in the 1970s, foreign minister in 1983 and deputy prime minister in 1983.
A former English teacher, he was the chief representative of Saddam Hussein’s regime to the rest of the world for two decades. Aziz was one of the few Christians in Saddam’s immediate entourage.
In 2003, shortly after the fall of Baghdad, he turned himself in to US forces.
In 2009 he was jailed for 15 years for the 1992 execution of 42 Baghdadi wholesalers and a seven-year sentence for his role in expelling Kurds from the north of the country.
His family have repeatedly called for his release, saying that he was suffering from heart and breathing problems, high blood pressure and diabetes.
In September his son, Ziad, said that the government wanted his father to die in Baghdad’s Kadhmiyah jail.