He was convicted in connection with the persecution of religious parties, a statement said.
Aziz, 74, served as foreign minister and deputy prime minister and was a close adviser to Saddam Hussein.
He has been previously convicted for his role in the execution of dozens of merchants for profiteering.
Aziz is reported to be seriously ill.
“The supreme criminal court issued an execution order against Tariq Aziz for his role in eliminating religious parties,” Iraqi state television reported.
Officials said two other defendants in the case were also sentenced to death – former interior minister Sadoun Shakir and former private secretary to Saddam Hussein, Abed Hamoud.
Aziz’s lawyer, Badee Izzat Aref, told the Associated Press that the verdict was “politically motivated”.
He said no decision about an appeal had been made yet.
“We are discussing this issue and what next step we should take,” he said.
Mr Aref, who is based in the Jordanian capital Amman, accused the Iraqi government of trying to divert attention from recent Wikileaks revelations which alleged that Iraqi forces had tortured prisoners.-BBC