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."
"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."
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.
Japan
Australia
