Top Iraqi Shia cleric dies of heart attack in Najaf
Funeral ceremonies will be held on Saturday in Najaf and its twin holy city of Karbala, a source within his office told AFP.
Al-Hakim "underwent surgery three days ago in hospital in Najaf and succumbed today to a heart attack", the source said.
Iraqi President Barham Salih in a statement paid homage to the "prominent figure" in Shia Islam.
The United States expressed its condolences in a statement from its embassy in Baghdad.
Al-Hakim will be buried in Najaf, home to the shrine of Imam Ali, the fourth Islamic caliph and relative of the Prophet Mohammed.
Born to a family of clerics in Najaf in 1936, Hakim was considered to be among the highest Shia religious authorities in the country.
At the time of his death, he was one of four ayatollahs of the Hawza, Najaf's Shia seminary, along with Grand Ayatollah Ali Al-Sistani, Iraq's top Shia cleric.
Al-Hakim was imprisoned between 1983 and 1991 under the regime of former dictator Saddam Hussein who feared neighbouring Iran's 1979 Islamic revolution would set off "a similar event" in Iraq, political commentator Marsin Alshamary said on Twitter.
A Shia clerical observer who asked to remain anonymous said that Al-Hakim set himself apart for his "closeness to the faithful", noting that he used to mix with pilgrims during Arbaeen, a key Shia commemoration.
"In public, he expressed no political opinion," the observer said, in line with the Shia theological school in Iraq that opposes the Iranian "Velayat-e faqih", which establishes religious authority over politics.