The NATO member state has curbed the flow of migrants - mainly refugees from wars in Syria and Iraq - into the bloc but Erdogan says he may review the deal after the vote.
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.
While state-run media reported Sunday night that roughly 51.3 percent of votes cast favored the constitutional changes, with 48.7 percent voting against, there was some uncertainty surrounding the tally.
"I sadly want to state that [the YSK] made this referendum questionable", he added.
Some 55 million people were eligible to vote on Sunday and results are expected to start coming in within hours.
Speaking at the Ankara headquarters of the ruling Justice and Development Party (AKP) Yildirim said: "I thank and express my gratitude to all our citizens who went to the ballot box with a high turnout, and who protected our democracy". He said all the constitutional changes would come into effect by November 2019.
"What is disconcerting for him [Erdogan] is not just the opposition, which is crying foul, but the fact that nearly 50 percent of the people voted against this massive change and may not be willing to accept the result easily", Aliriza said.
Few men can claim to have dominated politics in Turkey - or polarized his people - as much as Recep Tayyip Erdogan, the 63-year-old president who has urged his nation to approve reforms that will greatly expand his powers. "Yes, yes, yes. Our leader is the gift of God to us".
Firmino on target as Liverpool climb to third
There are some factors that suggest that is quite possible - West Brom have a small but nearly fully fit squad. "We defended well. Liverpool was the better team at The Hawthorns but almost got picked off late on in West Brom's only clear sight of goal.
Erdogan was voted to power in August 2014, the first time a Turkish President had been directly chosen by the popular vote.
Supporters found in him a man who gave a voice to the working- and middle-class religious Turks who had long felt marginalized by the country's Western-leaning elite. The result of the nationwide vote, which opposition parties are already contesting, sets in motion the most significant constitutional changes in the history of the Turkish Republic, allowing the next elected president vast new control over the country.
On Monday, many will be closely watching the initial assessment of the Organization for Security and Cooperation in Europe (OSCE), which had an observer mission in Turkey.
The vote comes as Turkey has been buffeted by problems.
Still, a widespread government crackdown has targeted followers of Gulen and other government opponents, branding them terrorists and a state of emergency imposed after the coup attempt remains in effect.
Erdogan made relations with the European Union a key issue in his referendum campaign, lambasting Brussels for failing to make progress on Ankara's stalled accession talks and trading Nazi jibes with Germany and the Netherlands when they barred pro-change rallies.
The country's foreign minister Mevlut Cavusoglu said this was the birth of a "truly new Turkey". Erdogan sent troops into Syria to help opposition Syrian forces clear a border area from the threat posed by Islamic State militants.
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