Hassan Khomeini, 43, a politically moderate cleric, will be the first member of the family of Iran's revolutionary founder to test his popularity at the ballot box.
In a conditional endorsement of the move, incumbent Supreme Leader Ayatollah Ali Khamenei told Khomeini last week he should be careful not to bring his grandfather's name into disrepute, a source close to Khomeini said.
Hardliners close to Khomeini have voiced concerns about Hassan Khomeini's candidacy, warning of the risk of a reformist alliance emerging at the top of Iran's political establishment.
Khomeini is 76, so the new assembly is expected to play a significant role in choosing his successor since its members are only elected every eight years.