The Republican People's Party (CHP), the main opposition party, has said that it will appeal to the constitutional court to prevent the referendum taking place.
AKP put forward the changes to the 1982 constitution, it said, in order to bring the country in line with European practices. The AKP is pushing for EU membership.
"The reform package has been approved by the parliament's general assembly," Mehmet Ali Sahin, the parliament speaker, said.
"Let it bring good things to our country."
Under the bill, the constitutional court will be expanded from 11 permanent and four substitute judges to a total of 17.
Currently the president selects three independently and the rest from a shortlist created by a group of senior judges.
The new proposals would see parliament select three judges and the remainder chosen by the president from a list created by a wider group of people.
Critics have said this gives too much power to the president and allows for AKP to install allies into judicial positions.
The constitutional court has frequently clashed with the AKP, which opposition parties accuse of seeking to undermine Turkey's secularist political system.
Also under the bill, military personnel could also be permitted to be tried in civilian courts for the first time and the power of military courts would be limited.
The army is traditionally seen as the guardian of the secular political tradition brought in by Kamal Ataturk, the nation's founder.
Legislators passed the bill just after 2am (23:00GMT) after a protracted session.
AKP has a majority in parliament and national elections are planned for 2011.