Twenty seven candidates are in the race, but incumbent Moncef Marzouki and anti-Islamist leader Beji Caid Essebsi are widely seen as the favorites.
The poll forms part of a political transition after the revolution that ousted Zine al-Abidine Ben Ali.
A parliamentary vote was held in October.
Tunisia – seen as the birthplace of the Arab Spring – is considered to have had the most successful outcome, with relatively low levels of violence.
Today’s election will deliver the country’s first directly elected leader since the removal of Zine al-Abidine Ben Ali. Most polling stations were opening at 08:00 and due to close 10 hours later.
If no candidate wins more than 50% of the vote, a run-off round will be held on December 31.
“We were the first to enter this cycle of change which they have called the Arab Spring,” PM Mehdi Jomaa was quoted as saying on the eve of the poll.
“We will be the first [to make the transition] but others will follow,” he added.
Beji Caid Essebsi, from the Nidaa Tounes (Tunisia’s Call) party, is the favorite to win after his party came first in the parliamentary election.
However, critics say Beji Caid Essebsi, an 87-year-old who served in the governments of post-independence leader Habib Bourguiba as well as Zine al-Abidine Ben Ali, represents the past.
Among the other candidates are Moncef Marzouki, parliamentary Speaker Mustapha Ben Jaafar, Republican Party leader Ahmed Nejib Chebbi, female magistrate Kalthoum Kannou and businessman Slim Riahi.
The Islamist party Ennahda, which led Tunisia’s last government but was beaten by Nidaa Tounes in October’s parliamentary election, did not field a candidate.
A statement from Ennahda leader Rachid Ghannouchi spoke of wanting “to avoid deepening polarization or dividing the country”. Ennahda’s rise had led to concerns among more secular-minded Tunisians that Islamists would dominate politics.
Tunisia is still facing the specter of civil unrest and terrorism, with Interior Minister Lotfi Ben Jeddou warning of “serious security threats” near the Algerian border where al-Qaeda militants are said to be hiding.
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