All MPs, except one who abstained from the voting, endorsed the text of the amendment which was okayed by the lower chamber - the House of Representatives - on Wednesday.
The amendment, which was agreed by major political parties in Bosnia, actually confirms the status which this northeastern city has enjoyed since the end of the war in Bosnia-Herzegovina.
Brcko is a self-governing, entity-neutral, administrative district under the sovereignty of the State of Bosnia-Herzegovina. The district has its bodies of authority and powers to adopt its own laws and regulations.
The amendment will go into force after its publication in the country's official gazette in the coming days.
Deputy High Representative Raffi Gregorian, who is also the international supervisor in the District of Brcko, and other international diplomats describe this as a historic step and the victory of peace for Bosnia-Herzegovina.
The mandate of the supervisor will end with the enactment of the constitutional amendment on Brcko.
The Brcko District was formed of the entire territory of the prewar municipality of Brcko.
The 1995 Dayton peace accords tailored Bosnia into two entities: the Serb republic and the Croat-Muslim federation, and the District of Brcko.
The enforcement of the amendment will bring an end to the mandate of the international supervisor in Brcko.