Khomeini, 43, the best-known of the former supreme leader's 15 grandchildren, has chosen to stand in the February 26 ballot after receiving broad support, the ISNA news agency reported.
"Hassan Khomeini, after the massive urging of different groups and after consulting various personalities, decided to register for Assembly of Experts elections," family member Seyed Ali Khomeini was quoted as saying today.
The mid-ranking cleric is considered a reformist in outlook and has close ties to that camp's most senior figures, such as Mohammad Khatami, who was president from 1997 to 2005.
In theory, it can dismiss him, and would be responsible for picking a replacement.
It would have the same task should Khamenei die.
Members are chosen by the public, for a term of eight years, from a list that is pre-screened by another powerful committee, the Guardian Council.
Both the Assembly and the Council are considered to be dominated by conservatives.
Khomeini's candidature follows a recent declaration that one of Iran's most senior clerics and its president from 1989 to 1997, Ayatollah Akbar Hashemi Rafsanjani, will again stand in the Assembly elections.
President Hassan Rouhani, a moderate, has faced vocal opposition from the present parliament, including on the nuclear deal.
Even so, MPs voted overwhelmingly to back the agreement despite failing to gain the right to oversee its implementation.
A less hostile parliament would give Rouhani a greater chance of passing at least limited social reforms, which he championed in his 2013 election campaign.
Like candidates to the Assembly, those wanting to become MPs have to be vetted by the Guardian Council.
The agreement should see all nuclear-related sanctions on Iran lifted in return for curbs and stronger international monitoring of its atomic programme.