More than 55.3 million Turks were eligible to cast ballots on sweeping changes to the president's role which, if approved, would grant Erdogan more power than any leader since modern Turkey's founder Mustafa Kemal Ataturk and his successor Ismet Inonu.
Polling closed at 1400 GMT and a vote count immediately began that should yield a clear result later today.
For the changes to be implemented the 'Yes' camp needs to win 50 per cent plus one vote.
Voting in Istanbul along with his family, Erdogan predicted that "our people would walk to the future" by making the right choice.
After a stamina-busting campaign that saw insults flung in both directions, Prime Minister Binali Yildirim said: "Whatever choice comes out on top, our nation will make the most beautiful decision."
The opposition has cried foul that the referendum has been conducted on unfair terms, with 'Yes' posters ubiquitous on the streets and opposition voices squeezed from the media.
"We are voting for Turkey's destiny," said the standard- bearer of the 'No' camp, Republican People's Party (CHP) leader Kemal Kilicdaroglu.
"God willing, the result will be auspicious and we will all have the chance to discuss Turkey's fundamental problems."
The co-leaders of Turkey's second largest opposition party, the pro-Kurdish Peoples Democratic Party (HDP) Selahattin Demirtas and Figen Yuksekdag, have been jailed on charges of links to Kurdish militants in what the party says is a deliberate move to eliminate them from the campaign.
Three people were killed in a shootout in the garden of a school used as a polling station in the southeastern Diyarbakir region, the Dogan news agency said, but it was not clear if the fighting was linked to the election or simply a family feud.
If passed, the new presidential system would dispense with the office of prime minister and centralise the entire executive bureaucracy under the president, giving Erdogan the direct power to appoint ministers.
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