Sadi Guven was speaking after the main opposition Republican People's Party (CHP) cited irregularities, including the use of unstamped ballot papers.
President Recep Tayyip Erdogan's push for an executive presidency succeeded with just over 51% of the vote.
The win was met with both celebrations and protests across Turkey.
The CHP has demanded a recount of 60% of the votes.
But Mr Guven told reporters on Monday the unstamped ballot papers had been produced by the High Electoral Board and were valid.
He said a similar procedure had been used in past elections.
Three of Turkey's biggest cities - Istanbul, Ankara and Izmir - all voted No to the constitutional changes.
Opposition supporters took to the streets of Istanbul to bang pots and pans - a traditional form of protest - in a series of noisy demonstrations.
Meanwhile, flag-waving supporters of Mr Erdogan celebrated as their president praised them for their "historic decision" that could keep him in office until 2029.
With 99.97% of ballots counted, the Yes campaign had won 51.41% of the votes cast, while No had taken 48.59%. Turnout was said to be as high as 85%.
Deputy Prime Minister Mehmet Simsek said there would be no early elections following the result.
The parliamentary vote would be held as scheduled in 2019, Mr Simsek told Reuters news agency.
Responding to Sunday's result, the European Commission issued a statement saying it was awaiting the assessment of international observers.
It urged Mr Erdogan to respect the closeness of the vote and to "seek the broadest possible national consensus" when considering the far-reaching implications of the constitutional amendments.
A similar call was made by Chancellor Angela Merkel of Germany.
"The tight referendum result shows how deeply divided Turkish society is and that means a big responsibility for the Turkish leadership and for President Erdogan personally," Mrs Merkel said in a joint statement with Foreign Minister Sigmar Gabriel.
A divisive campaign ended in a contested result. President Erdogan declared victory by a narrow margin and called on every side to respect it. But the opposition has not conceded, claiming voting irregularities. It's clouded the legitimacy of the mandate the president now feels he's been given, to concentrate political power in his hands.
International observers will give their verdict today - that could embolden or weaken the opposition's case and determine how Turkey's western allies will respond.
Mr Erdogan hoped this would be the crowning moment of his career. But it's left Turkey profoundly polarized, at risk of becoming another chronically unstable part of the Middle East.
"Today... Turkey has taken a historic decision," Mr Erdogan told reporters at his official Istanbul residence, the Huber Palace. "With the people, we have realized the most important reform in our history."
The president also said the country could hold a referendum on bringing back the death penalty - a move that would end Turkey's EU negotiations.