The defending continental champions, who had a four month FIFA ban lifted last month, will play in Group D along with World Cup-bound North Korea and United Arab Emirates.
Iraq captured the world's imagination by surprisingly winning the Asian Cup in 2007 but have struggled since.
"If we win again, I will run for president," Iraq captain Younis Mahmoud told reporters.
"We have a tough group. Iran are a tough side as are North Korea, who will have the World Cup experience behind them."
Iraq were banned in November for the second time in 18 months after the country's Olympic committee disbanded their football association (IFA) and government security forces seized control of the federation headquarters.
"We know that after the 2007 Asian Cup win, the team united the country more than the U.S. or any other country or politics could do," added Mahmoud.
"We will be aiming to win it again and regain the title and untie the country."
Australia, who defected to the Asian competition in 2007 and lost on penalties in the quarter-finals, must face fellow World Cup finalists and Asian heavyweights South Korea in Group C. India and Bahrain make up the group.
Japan and Saudi Arabia, both three-times winners of the tournament, are in Group B with Jordan and Syria.
Hosts Qatar face Kuwait, China and Uzbekistan in Group A.
Organisers said they expect full houses in the five stadiums and plan to offer "affordable packages" to attract thousands of overseas fans to the expensive gas-rich state.
Creating an attractive atmosphere is seen as vital to boosting Qatar's bold 2022 World Cup bid.
"I am confident new benchmarks will be set here in Doha next year. And one of the main reasons will be because of the players, coaches, referees, officials and fans will be eager to prove the future is Asia," said Asian Football Confederation president Mohammed bin Hamman.
The draw for the 15th Asian Cup was held in the Aspire Academy, the world's largest indoor sports training facility.
The tournament runs in Qatar from January 7-29.
Group A
Qatar
Kuwait
China
Uzbekistan
Group B
Saudi Arabia
Japan
Jordan
Syria
Group C
South Korea
India
Australia
Bahrain
Group D
Iraq
North Korea
United Arab Emirates
Iran
