Hassan Rouhani has been drawing attention recently for speaking publicly about the need to re-engage with the West, promising to release political prisoners and calling for greater reform of the media, the BBC reported.
Support for him has swelled following the withdrawal of Mohammad Reza Aref, who pulled out Tuesday on the advice of pro-reform ex-President Mohammad Khatami, leaving Rouhani as the only reformist candidate on the ballot.
Rouhani has the endorsement of Khatami and former President Akbar Hashemi Rafsanjani, who was disqualified by the powerful Guardian Council.
The remaining candidates are conservatives close to Supreme Leader Ayatollah Ali Khamenei.
About 50 million people are eligible to vote. Khamenei asked all Iranians to vote -- even those who did not like the Islamic system of government, the BBC said.
After casting his vote, the supreme leader spoke on state television.
"Inshallah [God willing], the Iranian people will create a new political epic," he said.
He also attacked U.S. criticism of the presidential election and those who said they did not recognize it.
"The Iranian people," Khamenei said, "will do what is in their interest."
On Wednesday he urged all Iranians to vote, even if their vote rejects Islamic rule
"Everyone must turn out," said Khamenei, who holds absolute power in Iran, "even if for reasons they don't want to support the Islamic ruling establishment."
He characterized voting as an act of patriotism.
Voters waited their turns in long lines outside mosques and schools. Dissident Ebrahim Yazdi, a former foreign minister, told the BBC, "I vote because I love Iran and I am faithful to the process of democracy."
If no candidate gets at least 50.1 percent of the vote to win outright, a runoff will be held June 21.
Friday's election is the first since 2009, when protesters demonstrated against results they said were fixed to favor Mahmoud Ahmadinejad, who is constitutionally barred from a third consecutive term.
No foreign observers will be monitoring the election, the BBC said.
Many reform newspapers have been shut down, journalists have been detained, and access to the Internet and foreign broadcasters restricted. The BBC said Iran warned 15 BBC Persian Service employees they must leave the BBC or their lives in London would be in danger
Tehran had no commented on the allegation.