Turkish President Recep Tayyip Erdogan called on foreign powers to respect the outcome of the referendum granting him extra powers, after a campaign marked by bitter tensions with the European Union.
"We would like other countries and institutions to show respect to the decision of the nation," he said, calling allies to now show greater awareness of Turkey's "sensitivities" in the "fight against terror".
Turkish Prime Minister Binali Yildirim declared victory for the 'Yes' camp in the referendum, saying the country had opened a "new page" in its democracy.
"The presidential system, according to unofficial results, has been confirmed with a 'Yes' vote," Mr Yildirim told supporters from the balcony of the headquarters of the Justice and Development Party (AKP) in Ankara.
"This is a decision made by the people. In our democracy's history, a new page has opened."
Unofficial results showed that 51.3% of Turks approved the changes to their constitution.
The 'Yes' vote will replace Turkey's parliamentary democracy with an all-powerful presidency and may see Mr Erdogan in office until at least 2029, in the most radical change to the country's political system in its modern history.
The outcome will also shape Turkey's strained relations with the European Union. The NATO member state has curbed the flow of migrants - mainly refugees from wars in Syria and Iraq - into the bloc but Mr Erdogan said he may review the deal after the vote.
Turkey should seek the broadest possible national consensus in its constitutional amendments, given the closeness of its referendum, the European Commission said.
"In view of the close referendum result and the far-reaching implications of the constitutional amendments, we also call on the Turkish authorities to seek the broadest possible national consensus in their implementation," the Commission said in a statement.
Broadcaster Haberturk said turnout was 86%. However, the opposition People's Republican Party (CHP) said a last-minute decision by the electoral board to accept unstamped ballots as valid votes put the vote in question.
"We will pursue a legal battle. If the irregularities are not fixed, there will be a serious legitimacy discussion," CHP deputy chairman Bulent Tezcan said.
The referendum has bitterly divided the nation.
Mr Erdogan and his supporters say the changes are needed to amend the current constitution, written by generals following a 1980 military coup, confront the security and political challenges Turkey faces, and avoid the fragile coalition governments of the past.
Opponents say it is a step towards greater authoritarianism in a country where around 40,000 people have been arrested and 120,000 sacked or suspended from their jobs in a crackdown following a failed coup last July, drawing criticism from Turkey's Western allies and rights groups.
Relations between Turkey and Europe hit a low during the referendum campaign when EU countries, including Germany and the Netherlands, barred Turkish ministers from holding rallies in support of the changes.
Mr Erdogan called the moves "Nazi acts" and said Turkey could reconsider ties with the European Union after many years of seeking EU membership.