Dozens of men and women, in separate queues, were seen outside polling stations as they opened at 8:00 am (0330 GMT). Voting continues until 6.00 pm but that could be extended if there is a big turnout.
More than 50.5 million people are eligible to vote for the man -- no women candidates were approved -- to succeed Ahmadinejad, who is barred from standing for a third consecutive term under the constitution.
Iran's supreme leader Ayatollah Ali Khamenei, who has called for a large turnout but not publicly stated his preference for any single candidate, voted early.
"Inshallah (God willing), the Iranian people will create a new political epic. I advise all people to vote," said the Iranian leader after casting his ballot.
He also attacked US criticism of the credibility of the presidential poll.
"The hell with you... " who do not agree with the way the election is being run, Khamenei said on national television. "The Iranian people... Will do what is in their interest."
If no candidate secures more than half of the votes to win outright today, a second round will be held a week later.
The first results are expected tomorrow.
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