The document was approved in a second reading and will be submitted to the president for signature, after which it will become a law. Turkish leader Abdullah Gul earlier said he would approve the draft law.
A total of 411 MPs out of 550 voted for the controversial bill, with 367 votes required to amend the constitution.
The initiative was sponsored by the ruling Justice and Development Party. The party has been accused by its opponents of possessing a hidden Islamic agenda due to the suspected connections of many of its MPs with outlawed Islamist groups.
The Turkish opposition however sees the initiative as a dangerous move which could undermine Turkey's status as a secular state and encourage radical Islamist groups, and it said it would turn to the Constitutional Court should the bill be finally approved.
The headscarf issue is a source of tension in predominantly Muslim Turkey. Almost two-thirds of Turkish women currently wear a headscarf and many of them stopped attending universities after the traditional Islamic covering was banned on campuses in 1989.
