The reform proposes that Turkey's president should be directly elected by a popular vote for a five-year term, renewable for a further five years.
Parliament now elects the president for a non-renewable seven-year period.
The ruling centre-right AK Party decided to push the reform in a direct appeal to voters after losing a battle with Turkey's secular elite, which includes army generals and top judges, over a presidential election in parliament.
Parliament has now postponed the presidential contest until after a July 22 general election.
Sezer will stay in office in an interim capacity until his successor can be chosen.
The political turmoil has unnerved financial markets.
AK has said it may take the presidential election issue to a referendum if Sezer or the courts block it. Opinion polls show strong public support for the reform.
Other amendments approved by parliament on Thursday include reducing parliament's term to four years from five.
Lawmakers also approved measures that would make it more difficult for the pro-Kurdish Democratic Society Party (DTP) to field candidates as independents in an effort to circumvent Turkey's high 10 per cent threshold for entering parliament.