About 55 million people were eligible to vote across 167,000 polling stations, and turnout is said to have been high.
Just over 51 percent of voters have opted for a constitutional change to grant sweeping powers to the president.
The president said the "Yes" camp had secured 25 million votes in the referendum, 1.3 million ahead of "No" votes.
Erdogan supporters say replacing the parliamentary system with an executive presidency would modernise the country.