Ayatollah Mahdavi Kani was appointed after 63 members of the body voted in favor of him on Tuesday morning.
The Assembly of Experts consists of 86 clerics elected by the public to eight-year terms.
The body is tasked with electing a new leader in the event of the passing of the Leader of the Islamic Revolution.
The Assembly was headed by the veteran revolutionary figure and two-term former president Ayatollah Ali Akbar Hashemi Rafsanjani.
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Ayatollah Rafsanjani, who headed the Experts Assembly for several years, declined to stand as candidate for the position and supported Ayatollah Mahdavi Kani's candidacy.
Iran's Assembly of Experts is responsible to supervise the performance of the Leader. The 86-man body can elect or dismiss the Leader.
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