The 'Yes' campaign won 63.2 per cent of the vote while the 'No' campaign mustered 36.8 per cent, the election commission said in figures quoted by the NTV channel, in an initial count based on 25 per cent of the ballot boxes.
The result could still change as more ballot boxes are counted across the hugely diverse country following the close of polls at 0730 IST.
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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.
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."
Yildirim was later due to address supporters from the headquarters of the Justice and Development Party (AKP) in Ankara while Erdogan was due to watch the results in Istanbul.
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.
The poll is also taking place under a state of emergency that has seen 47,000 people arrested in an unprecedented crackdown after the failed putsch of July last year.
"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.
Closely watched tomorrow will be the initial assessment of the international observer mission of the OSCE Office for Democratic Institutions and Human Rights (ODIHR) and the Parliamentary Assembly of the Council of Europe (PACE).
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