The yes obtained 51.4% of the votes against 48.6% of the no, with 99.5% of the polls being screened, according to unofficial results published by the pro-government press agency Anadolu.
In the evening, the head of the High Electoral Council (YSK) of Turkey, Sadi Güven, confirmed that he had won. He added however that the final result would be announced: "in 11 or 12 days."
According to the YSK, the participation rate was 85%, and the yes-ahead rate was 1.25 million votes, with 600,000 remaining ballots remaining.
"Today ... Turkey has made a historic decision," Erdogan said. "With the people, we have made the most important reform of our history," added the head of state, who called on foreign countries to "respect" the outcome.
Shortly thereafter, the Turkish president mentioned the possibility of organizing a new referendum, this time on the reinstatement of the death penalty, which would put an end to Turkey's accession to the European Union.
"With this vote, we have opened a new page for our democracy," Prime Minister Bilali Yildirim said at his AKP party's headquarters in Ankara.
Erdogan's fans celebrated the victory with Turkish flags, although they admitted they expected a less narrow result.
"To be honest, we did not expect this result but it does not matter. It's still a good result," said Derya, 25.
But the first data on the vote indicate that the country is totally divided over the proposed constitutional changes.
He did not triumph in Istanbul, Ankara and Izmir, the country's three largest cities, as well as in the Kurdish-majority regions and in the coastal areas of the Mediterranean and the Aegean. He did have his greatest support in the regions of Anatolia.
"It is a victory for Erdogan, but it is also a defeat. He lost in Istanbul, where he started his political career" as mayor in 1994, wrote on Twitter Soner Cagaptay, the Turkey expert at the Washington Institute.
'Manipulations'Turkey's two main opposition parties denounced "manipulations" and announced their intention to call for a new recount.
Both formations strongly denounced a measure announced at the last moment by the Turkish High Electoral Council (YSK) to consider valid votes that did not bear the official seal of the polling station in which they were entered in the ballot box.
The head of the main opposition party, the CHP (Social Democrat) Kemal Kiliçdaroglu, said that this change "had called into question the legitimacy of the referendum."
The CHP announced through one of its leaders that it questioned the votes coming from almost 37% of the polls. This could reach 60%, said Erdal Aksünger, deputy secretary-general of the party.
"Believe me, this referendum is not over," Aksünger told CNN Turk, quoted by the Dogan news agency. "It's totally invalid," he said.
For its part, the second party of the opposition, Prokurdo HDP, announced on Twitter that it will contest the votes coming from "two-thirds" of the polls. "The data that comes to us indicates that there is a manipulation of the order of 3 or 4 percentage points," he said.
Some 55.3 million voters were called to vote on a constitutional review that changes the current parliamentary system by a presidential system.
The reform includes, in particular, the abolition of the post of prime minister in favor of a president who would concentrate ample prerogatives.
Drastic restructuringFollowing the announcement of Erdogan's victory, the European Union urged the Turkish government to seek the "greatest possible national consensus" to implement the changes, in a joint statement by European Commission President Jean-Claude Juncker, the head of European diplomacy, Federica Mogherini, and the European Commissioner for Enlargement Negotiations, Johannes Hahn.
Council of Europe Secretary-General Thorbjorn Jagland said that "in view of the close results", Turkish leaders "should consider next steps wisely."
With this constitutional reform, Erdogan, 63, who overcame an attempted coup nine months ago, could remain in power until 2029.
But his detractors see in it a new authoritarian turn of a man whom they accuse of wanting to silence any criticism, especially after the failed coup d'etat, from which governs the country in the state of emergency.
About 47,000 people have been arrested and more than 100,000 have lost their jobs or are suspended.