The 85-year-old was under medical care and hospitalised days ago due to a "digestive disease" at a Tehran hospital, IRNA said, citing a statement from his office.
A veteran revolutionary close to Khamenei, Mesbah-Yazdi was also known as a staunch supporter of ultraconservative former president Mahmoud Ahmadinejad.
However, he lifted his support for the firebrand president during his second term due to his "deviation" after Ahmadinejad had a falling out with the supreme leader.
At the time of his death, Mesbah-Yazdi was the head of the of Imam Khomeini Education and Research Institute and a long-time member of the Assembly of Experts, the body that oversees the works of the supreme leader and is tasked with choosing his successor.
He had failed to secure a seat in the assembly in the 2016 elections amid a surge by reformists and moderates, whom he fiercely opposed, but managed to regain the position in a by-election two years later.
The cleric had said in 2014 that Iran's people "do not deserve such a leader" as Khamenei and that his leadership was a "blessing" for the Islamic republic, ISNA news agency reported.
Iran's President Hassan Rouhani and parliament speaker Mohammad-Bagher Ghalibaf in separate statements offered their condolences on Mesbah-Yazdi's death to the nation of Iran, his family and the supreme leader.
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