Erdogan, a pious Muslim, has ruled Turkey as premier since 2003, a period in which he has transformed the country with modernisation projects but also faced accusations of a gradual religious conversion of society and an erosion of civil rights.
Polls opened at 0500 GMT and are due to close at 1400 GMT.
The polls are the first time Turkey will directly elect its president, who has previously been chosen by parliament and in recent decades has fulfilled a largely ceremonial role.
However Erdogan, who is happy to be referred to by followers as the "Sultan", has made clear he intends to be a head of state who "sweats" and exercises real power.
His ruling Justice and Development Party (AKP) has vowed to seek to change the constitution to give the president more powers, which could give Turkey a presidential system similar to France rather than its current parliamentary democracy.
Yet his opponents accuse Erdogan of undermining the secular legacy of Turkey's founding father Mustafa Kemal Ataturk, who based the modern state after the collapse of the Ottoman Empire on a strict separation between religion and politics.
Opinion polls predict that Erdogan will easily win over 50 percent of votes to take Ankara's Cankaya presidential palace in the first round, with his main opposition rival Ekmeleddin Ihsanoglu lagging far behind in second place.
"There really is no uncertainty about this outcome. It's almost a foregone conclusion that Erdogan will win," said Sinan Ulgen of the Carnegie Centre.
While many secular Turks detest Erdogan intensely, he can still count on a huge base of support from religiously conservative middle-income voters particularly in central Turkey and poorer districts of Istanbul who have prospered under his rule.
"We will write the history of the new Turkey on August 10," he told tens of thousands of cheering supporters in Ankara in one of his final election rallies.
Out of a population of some 76 million, 53 million voters were to cast their ballots at more than 165,000 pollings stations.
Results are expected to come in rapidly and many suspect Erdogan is already planning a victory speech from the balcony of AKP headquarters in Ankara around midnight.
Erdogan over three months has spearheaded a lavish and immense campaign that has swamped the efforts of his rivals, holding mass rallies in almost 30 Turkish cities as his face glared on gigantic billboards at pedestrians in Istanbul at almost every street corner.
"National will, national power," reads his main election slogan.
Erdogan's main campaign advertisement - which had to be edited after a court ruled images of a woman praying violated Turkey's secular rules - has saturated national TV and shows the "people's president" leading thousands of ordinary Turks into the Cankaya.
The campaign of Ihsanoglu - a bookish former head of the Organisation of Islamic Cooperation (OIC) - has been modest by comparison and Erdogan has gleefully belittled his main rival as a dreamy academic who will get nothing done.
The third candidate Selahattin Demirtas, from Turkey's Kurdish minority, has shown considerably more dynamism and his charisma, flashing grin and fondness for white shirts with rolled-up sleeves have led him to be dubbed the "Kurdish Obama" in some quarters.
Yet Demirtas' campaign will be considered a success if he musters over 10 percent of the vote.
Erdogan endured the toughest year of his rule in 2013 and was shaken by deadly mass protests sparked by plans to build a shopping mall on Gezi Park in Istanbul that grew into a general cry of anger by secular Turks who felt ignored by the AKP.
Later in the year, stunning corruption allegations emerged against the premier and his inner circle, including his son Bilal based on bugged conversations that enthralled the country like a soap opera.
But Erdogan has come out fighting, denying the allegations and blaming a former ally turned rival, the Pennsylvania-based Turkish cleric Fethullah Gulen for launching a plot against him.
He has behaved at rallies as much like a prize fighter as a politician, aiming punches at foes like Gulen or even a critical female Turkish journalist who he denounced as a "shameless" woman.
With the election campaign coming amid Israel's offensive in the Gaza Strip, Erdogan caused huge controversy outside of Turkey by saying the Jewish State was behaving even worse than Adolf Hitler.
If he wins, Erdogan will in late August take over as president from Abdullah Gul, a co-founder of the AKP who appears to have taken a distance from the pugnacious premier and whose political future is unclear.
There will be great scrutiny on who Erdogan decides should be the new premier with Foreign Minister Ahmet Davutoglu seen as a possible choice.
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This guy has done nothing to save muslims in palestine. Other than talk there is nothing. Some rulers talks more than others and therefore erdogan wins. But no action behind the talks or words. Its all empty.