"Following a call by some grand ayatollahs to mourn the death ... we announce tomorrow, Monday, December 21, a day of public mourning," Mousavi and Karroubi said in a joint statement.
"We invite all saddened religious people mourning the death of this pride of the Shia world to take part in the funeral of this legend of endeavour, jurisprudence and spirituality."
Montazeri will be buried in the shrine of Masoumeh, a revered Shia figure, in Qom, his office said.
"He didn't fear expressing his views, critical of the current supreme leader or the policies of the government"
Iranian journalist and author
Foreign media are banned from covering the ceremony.
"Thousands of people from Isfahan, Najafabad, Shiraz and other cities have left for Qom to take part in his funeral," Parlemannews.ir, the website of the parliament's reformist faction, reported.
Videos posted on the internet purported to show hundreds of Montazeri's supporters taking to the streets of Najafabad, his birth town, to mourn his death.
Shops in the town were closed and cloaked in black cloth pinned with pictures of the late cleric.
Baqer Moin, an Iranian journalist and author, told Al Jazeera that Montazeri's absence would be "greatly felt across the country", among people on both sides of the political divide.
"He was the most heavyweight among them [the reformists]. He had great popularity because he was a humble man, he was a simple man ... and above all he was very courageous," Moin said.
"He didn't fear expressing his views, critical of the current supreme leader or the policies of the government."
In August, Montazeri described the clerical establishment as a "dictatorship", saying that the authorities' handling of street unrest after the disputed re-election of Mahmoud Ahmadinejad "could lead to the fall of the regime".
|Montazeri criticised authorities of their handling of the disputed election aftermath
"I hope the responsible authorities give up the deviant path they are pursuing and restore the trampled rights of the people," he wrote.
"I hope authorities ... have the courage to announce that this ruling system is neither a republic nor Islamic and that nobody has the right to express opinion or criticism," he said.
State news agency IRNA called Montazeri the "clerical figure of rioters" in its early reports of his death and dropped his clerical title of Grand Ayatollah.
Ghanbar Naderi, a journalist for the Iran Daily newspaper, told Al Jazeera: "This is huge blow to the reformist camp, because he is unreplaceable and nobody is happy to hear about his sad demise.
"He used to say that religion should be separated from politics, because in this way, we can keep the integrity of religion intact."
But Seyed Mohammad Marandi, a political analyst at the University of Tehran, told Al Jazeera in August that Montazeri said "the same thing for around 25 years".
"After his inner circle was discovered to be linked to Mujahidin terrorists based in Iraq, he was isolated by the reformists," he said.
"He is not a major player and has always been very critical," Marandi said.
Ayatollah Ali Khamenei, Iran's supreme leader, offered condolences to his family, despite Montazeri criticising him and questioning his credentials for being the country's highest religious authority.
"He was an accomplished theologian and a prominent teacher who spent a large part of his life for Imam's [Khomeini's] cause," he said in a statement carried by state television's website.
Montazeri had at one time been expected to succeed Khomeini, but he fell from favour in the 1980s.
The cleric had long been critical of the concentration of power in the hands of the supreme leader and called for changes to the constitution, which he helped draw up after the 1979 Islamic revolution, to limit his authority.