The package of 18 amendments would abolish the office of prime minister and give the president authority to draft the budget, declare a state of emergency and issue decrees overseeing ministries without parliamentary approval.
The "Yes" campaign had won 55.5 percent of the vote while the "No" campaign had mustered 44.5 percent, the election commission said in figures quoted by state news agency Anadolu, in an initial count based on 65 percent of the ballot boxes.
Erdogan and his supporters had argued the "Turkish-style" presidential system would bring stability and prosperity in a country rattled by a failed coup a year ago that left more than 200 people dead, and a series of devastating attacks by the Islamic State group and Kurdish militants.
The referendum campaign was dominated in its last days by debates over a possible federal system in Turkey after Erdogan's advisor Sukru Karatepe suggested, if approved, the constitutional changes could lead to federalism.
President Recep Tayyip Erdogan, who called the referendum and has championed the "yes" campaign, says the proposed "Turkish style" presidential system will ensure the country no longer risks having weak governments.
Detractors warn that the changes could lead to an autocratic, one-man rule by President Recep Tayyip Erdogan.
"We need to make a decision that is beyond the ordinary", Erdogan said.
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The main opposition leader Kemal Kilicdaroglu of the Republican People's Party (CHP) cast his vote in Ankara.
According to the first preliminary results, the "Yes" vote is leading in the Turkish referendum on constitutional changes allowing for an expansion of presidential powers.
If officially confirmed, Sunday's outcome is expected to have a huge effect on Turkey's long-term political future and its global relations.
The President had earlier said, "God willing I believe our people will decide to open the path to much more rapid development".
The constitutional changes have been discussed since Erdogan was voted president in August 2014.
Devlet Bahceli, leader of the Nationalist Movement Party (MHP) which has backed the changes, said he hoped the vote would be a "major turning point in the life of our people and in Turkey".
The data showed that Turkey's three biggest cities Istanbul, Ankara and Izmir, as well as the predominantly Kurdish southeast voted "No", however, "Yes" campaign still performed better than expected in southeast where the region heavily voted for pro-PKK HDP in the general elections in 2015.
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"Up until I voted I was undecided but the recent terror events wore our people down".
They say they do not want "one-man rule" in the country and are afraid Turkish society will become more polarised among political lines.
The poll took place under a state of emergency that has seen 47,000 people arrested in an unprecedented crackdown after the failed putsch of July a year ago.
The crackdown saw roughly 100,000 people lose their jobs, including judges, lawyers, teachers, journalists, military officers and police.
They also say it would strengthen the government's hand in the fight against terrorism, and bring more stability and prosperity for the country by giving it free rein to institute reforms. Hundreds of media outlets and nongovernmental organizations have been shut down.
The two had a falling out that year, and Erdogan has blamed Gulen for orchestrating the 2016 coup attempt.
Relations between Turkey and Europe hit a low during the referendum campaign when European Union countries, including Germany and the Netherlands, barred Turkish ministers from holding rallies in support of the changes.
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