From the airport the body is to be taken to the mausoleum of Imam Kadhim in the Kadhimiya shrine district of Baghdad.
It was later due to be taken to an official mourning ceremony in the fortified Green Zone, the seat of the Iraqi government and the US embassy.
Burial in Najaf
After the ceremony in the Green Zone, the body will be conveyed to the Shia Muslim shrine city of Karbala.
Al-Hakim is expected to be buried in Najaf on Saturday.
Condolences were painted on black banners that hung from the main streets of the city, and hundreds gathered near al-Hakim's office and his family home to pay respects.
The Iraqi government announced a three-day mourning period, beginning on Thursday.
Al-Hakim helped to establish an opposition movement in 1982 while in exile in Iran to fight the Sunni-dominated government of Saddam Hussein, Iraq's executed former leader.
He spent nearly two decades in Iran during Saddam's rule and returned only after the US-led invasion of 2003.
His Islamic Supreme Council of Iraq swept Shia areas in the first provincial elections after the invasion, but in new elections this January the party suffered major losses.
Ayatollah Ali al-Sistani, Iraq's most senior Shia religious leader, was deeply saddened by al-Hakim's death, his office in Najaf said.
"In deep sadness, Ali al-Sistani received the news of the death of his eminence scholar Abdel Aziz al-Hakim, who passed away after a life full of giving for the sake of his religion and country, and to save his people from despotism and injustice," al-Sistani's office said.
In Tehran, Ayatollah Ali Khamenei, Iran's supreme leader, praised al-Hakim on Thursday as the symbol of the struggle against Saddam's government.
|Al-Hakim's death comes amid a surge in violence in Baghdad and other cities [AFP]
"His death is a big loss for the Iraqi people and government, and is a painful incident for the Islamic Republic [of Iran]," Khamenei said in a message read at a ceremony in Tehran.
"He symbolised the hardship involved in jihad in fighting tyranny.
"The efforts and endeavour of this hardworking cleric are unique and unforgettable both in Iraq and Iran."
In Damascus, Bashar al-Assad, the Syrian president, expressed his "sincere condolences and sympathy" to his Iraqi counterpart, Jalal Talabani, and to the people of the country.
A former chain smoker, al-Hakim was admitted to Tehran's Masih Daneshvari hospital on Saturday following complications.
Al-Hakim had been in Tehran for treatment for more than four months and also visited the US in the past to consult lung cancer specialists.
Al-Hakim's death coincides with a resurgence of violence across Iraq, including a devastating attack on two ministry buildings inside the Green Zone.
Series of attacks
There was no respite from the violence on Thursday. At least one person was killed and 22 others wounded after several car bombs exploded in Baghdad.
The bombs mainly targeted Iraqi troops in the city and a northern suburb, officials said.
The deadliest bombing struck at about 11am near a US military base close to Taji, north of Baghdad, killing one person and wounding six others, an Iraqi police official said.
Hours earlier, three bombs attached to parked cars exploded in Baghdad's Azamiya neighbourhood, wounding four police officers and two civilians.
Two more bombings struck later in the day in different parts of Baghdad, wounding 10 people, police said.