Turkey has begun counting votes for the referendum which will ultimately determine whether or not to expand Erdogan's power as he requested.
As Mr Erdogan's supporters celebrated on the streets of Istanbul with fireworks, the Republican People's Party said "illegal acts" were carried out in favour of the government in the referendum.
The European Commission has called on Turkey to seek a national consensus following a referendum result that will substantially increase the powers of the office held by President Recep Tayyip Erdogan.
"It is the first time in the history of Turkey that the parliament and people decided on such an important change".
The president struck a conciliatory tone, thanking all voters regardless of how they cast their ballots and describing the referendum as a "historic decision".
During the referendum campaign, Erdogan lashed out at Germany and the Netherlands, accusing them of acting like the Nazis when they barred rallies for the "Yes" camp.
Saturn's moon boasts all the ingredients for life
An illustration of NASA's Cassini spacecraft flying through the water plumes of Enceladus, an icy moon that orbits Saturn. A photo from October 14, 2015 taken by NASA's Cassini spacecraft shows the north pole of Saturn's icy moon Enceladus.
After calculation of 99% of ballots, 51.3% of the citizens voted for the package of amendments to the constitution of the republic that introduced the presidential form of government.
The changes allow the president to appoint ministers, senior government officials and half the members of Turkey's highest judicial body, as well as to issue decrees and declare states of emergency.
The main opposition party, however, is contesting what it says around 37 percent of ballot boxes and that could be well over 2 million votes in there.
The country's pro-Kurdish party said it may take the case to the European Court of Human Rights if the electoral board does not reverse his decision and nullify the ballots lacking the official stamps. Under the changes, President Erdogan could stay in power through 2029. Manfred Weber, leader of the center-right grouping, said Erdogan was splitting his country, while the co-leader of the Green MEPs, Ska Keller, said the result was "a devastating blow to democracy in Turkey".
The "yes" means Turkey's constitution to be amended to replace the parliamentary system, scrap the office of the prime minister and transform the presidency from a ceremonial position to an executive one.
Proponents of the reform argue that it would end the current "two-headed system" in which both the president and parliament are directly elected, a situation they argue could lead to deadlock. "There are no losers in the referendum, the entire nation won from it", Binali Yildirim said. A win neuters parliamentary oversight over the president's decisions.
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