Six candidates are in the running.
If no candidate gets more than 50 percent of the vote, there will be a runoff election June 21.
Press TV said polls have shown a runoff will be likely.
About 50 million Iranians are eligible to vote in a process that will end Ahmadinejad's presidency after eight years. About 66,000 polling stations will be open across the country.
The six candidates had a final day of campaigning Thursday. Severe restrictions were imposed on foreign and local media to ensure coverage of the elections remains under control, Britain's Guardian reported. The newspaper said most visa applications filed by foreign news organizations to cover the elections were rejected or ignored.
The other four candidates are Hassan Rohani, president of the Expediency Council's Center for Strategic Research; Saeed Jalili, secretary of the Supreme National Security Council; Ali Akhbar Velayati, former foreign minister; and Mohammed Gharzi, former minister of telecommunications, Press TV said.
Rezaei was the commander of the Iranian Revolutionary Guards Corps from 1981 to 1997, Mehr News said.
Velayati was foreign minister for 16 years. Jalili is Iran's chief nuclear negotiator.
Gholam al-Haddad-Adel, former Parliament speaker, and Mohammed Reza Aref, former first vice president, withdrew from the race earlier this week, Press TV said.