With 98 percent of ballots counted, Turks approved the most radical constitutional overhaul since the republic was founded 93 years ago by 51.3 percent to 48.7 percent, according to the state-run Anadolu news agency.
Foreign Minister Mevlut Cavusoglu voted in southwestern Antalya province.
President Recep Tayyip Erdogan, who has been the country's preeminent politician for the last decade-and-a-half has consolidated personal power, stripped away checks and rivals inside the courts and the government and unleashed an unprecedented crackdown affecting almost all spheres of public life following a failed coup attempt in July of past year.
Opponents argue that the changes will effectively lead to one-man rule and autocracy with Erdoğan at the helm.
At a rally in Istanbul, one of four he held in the last hours before Sunday's vote, Erdogan described the constitutional proposals as the biggest change in Turkey since the country was established almost a century ago, and the culmination of the response to July's abortive putsch.
"Because we must make an out-of-the-ordinary choice in order to attain the level of modern civilisations envisaged by the hero Mustafa Kemal", the president said, referring to modern Turkey's founder Mustafa Kemal Ataturk. Kemal Kilicdaroglu, leader of the main opposition Republican People's Party, asked supporters in the capital, Ankara.
The proposed constitutional changes seek to transform Turkey's governance from a parliamentary system to an executive presidency, significantly expanding the powers of the top office.
If the Yes vote prevails, the 18 constitutional changes will convert Turkey's system of government from parliamentary to presidential.
After serving as Prime Minster for more a decade, Erodgan became President in 2014.
Turks have backed President Recep Tayyip Erdogan's call for sweeping new presidential powers, partial official results of a referendum indicate.
The outcome is expected to have a huge effect on Turkey's long-term political future and its worldwide relations.
At a polling station in the southeast, two people were shot dead. Voting against them is being publicised by the ruling party and President Tayyip Erdogan as "support for terrorism".
"However, "Yes" campaigners argue that such extensive powers are necessary to keep political, economic and security crises at bay, and that concerns over dictatorships and authoritarian regimes are unwarranted.Muttalip Meric, a postgraduate student who voted "Yes", told MEMO that such fears were baseless".
Opponents have warned the new system will send Turkey lurching towards dictatorship as it would concentrate unchecked power in the hands of Mr Erdoğan, who has jailed opponents and cracked down on dissent since a failed coup against him past year.
The vote comes as Turkey has been buffeted by problems. "A one-man system is like that", said Istanbul resident Husnu Yahsi, 61, who said he was voting "no".
The crackdown saw roughly 100,000 people lose their jobs, including judges, lawyers, teachers, journalists, military officers and police.
But Erdogan himself denied the comments in a public rally this week after an angry backlash from his major ally the right-wing Nationalist Movement Party (MHP), saying that any federal system was off the table. Nearly all opposition media have been shut down and "now there is only state-run news agency Anadolou that is going to report this all", the journalist argued.
Erdogan has also blasted European countries, accusing the Netherlands of Germany of being Nazis after authorities there refused to allow Turkish ministers to hold rallies to woo expatriate voters for the referendum.
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