Currently, the president is elected to a single seven-year term by parliament.
Another clause of the package envisages general elections for every four years instead of the current five.
Initial results are not expected until late on Sunday.
People in the dark
With no public debate on the constitutional reforms, however, media interviews with people on the street show that Turks have very little knowledge on their actual content and that some do not even know that a referendum is taking place.
The ruling Justice and Development Party (AKP), which drew up the reforms, is expected to easily garner the necessary support in the vote, thanks to the 47 per cent of the vote the party obtained in general elections less than three months ago.
The AKP rushed the package through parliament in May after an army-backed secularist campaign blocked the party from choosing one of its own – Abdullah Gul, a politician with Islamist roots – as president.
But snap general elections on July 22 called to resolve the crisis handed the AKP a landslide victory, allowing the party to easily secure Gul’s elections the following month.