A large banner with the image of Iran's slain supreme leader Ayatollah Ali Khamenei adorns a main taxi rank close to Tajrish Square in Tehran. AFP
"The vote to appoint the leader has taken place and the leader has been chosen," said Ahmad Alamolhoda, a member of the Assembly of Experts, as quoted by Iran's Mehr news agency.
He said the secretariat of the body will announce the name later.
Other members confirmed the decision, with one suggesting the son of late supreme leader Ali Khamenei will take the post.
Mojtaba Khamenei has been touted as a possible successor to his father, who became supreme leader in 1989.
The position is the highest political and religious authority in Iran and has the final say on all matters of state.
Mohsen Heydari, who represents Khuzestan province in the selection body, said "the most suitable candidate, approved by the majority of the Assembly of Experts, has been determined", according to Iran's ISNA news agency.
"The 'Great Satan' has also mentioned the name of the choice made by the representatives," he added, in reference to the United States.
US President Donald Trump has insisted he should have a role in picking the next leader and has rejected the possibility of Mojtaba Khamenei filling the role, dismissing him as a "lightweight".
Iranian officials have categorically rejected the notion that Trump would have any role in choosing a successor.
Another member of the assembly, Mohammad Mehdi Mirbagheri, confirmed in a video carried by Iran's Fars news agency that "a firm opinion reflecting the majority view has been reached".
Supreme leader Ayatollah Ali Khamenei was assassinated on February 28 during US and Israeli strikes on Iran, in the first day of a war that has spread across the Middle East.
On Sunday, the Israeli army threatened to "target" members of the assembly choosing the new leader.
"We warn all those considering taking part in this meeting to select the successor that we will not hesitate to target you," it said in a post.
But Mirbagheri insisted members of the body were proceeding as planned, saying they were doing so with precision as "the current circumstances are difficult and obstacles remain".
Short link: