His body was to be flown from the Iranian city of Qom, a seat of Shia learning about 100km south of Tehran, to Iraq, Iranian state media reported.
A day earlier, Mahmoud Ahmadinejad, the Iranian president, called al-Hakim's death "a great loss for the Iraqi people".
He paid particular tribute to al-Hakim's family, describing them as "revolutionaries", the official IRNA news agency reported on Wednesday.
Al-Hakim, the leader of the Supreme Iraqi Islamic Council (SIIC), one of Iraq's most powerful Shia parties, spent nearly two decades in Iran during the rule of Saddam Hussein, Iraq's executed former leader.
In 1982, he helped to establish an opposition movement in exile in Iran to fight Saddam's Sunni-dominated government, and returned to Iraq after the US-led invasion of 2003.
The SIIC is currently part of Iraq's ruling Shia alliance, which includes the Dawa party of Nouri al-Maliki, the prime minister, but earlier this week announced it was joining a new alliance for elections next January.
Much of the SIIC's support comes from the influence of the al-Hakim name, which is revered among Shia Muslims for its lineage of scholars and sacrifice during the rule of Saddam Hussein.