President Recep Tayyip Erdoğan on Sunday evening called ruling Justice and Development (AK) Party leader and Prime Minister Binali Yıldırım and Nationalist Movement Party (MHP) chairman Devlet Bahçeli and Grand Unity Party (BBP) chairman Mustafa Destici to congratulate them over the referendum victory.
The president also thanked the voters who went to the polls to reflect their choice.
In return, Bahçeli, who supported the "yes" campaign in Sunday's vote, said that the outcome of the referendum was an "undeniably successful achievement" that should be respected.
Meanwhile, many world leaders sent congratulatory messages to Erdoğan, presidential sources said.
As of 9.25 p.m. (1825GMT), unofficial results showed Yes in the lead with 51.34 percent -- 24,789,242 votes -- and No at 48.66 percent with 23,499,390 votes.
Sunday's referendum asked voters to say 'Yes' or 'No' to an 18-article bill that would see the country switch from a parliamentary to a presidential system, among other changes.