The ultimate aim is to prevent the two houses of parliament, the lower house, or Bundestag and the upper house, or Bundesrat, from neutralizing each other, by mapping out more precisely what each side is responsible for.
The reform entails some 20 amendments to the constitution and is designed to streamline the country's cumbersome federalist system, making it easier to pass new laws and prevent gridlock.
The bill, which passed the Bundestag by the necessary two-thirds majority after years of bitter infighting, must now win the approval next week of the Bundesrat, which represents Germany's 16 federal states.
Cornerstone of wider reform package
The revamp is seen as the cornerstone of a package of reforms agreed on in principle by Chancellor Angela Merkel's left-right government when it took power in November.
Ahead of the vote, Merkel had met with the state premiers of the country's 16 "Länder" or federal states.
"This is one of the most important reforms of our time," she told deputies. "With this project, we prove our courage to change."
Their positions are not under threat from the federal reforms, and in some areas their authority will actually be enhanced. The new measures are also good news for the chancellor, because they restrict the veto powers of the regions.
The government will now be able to push through a lot more legislation without requiring the support of the federal states. However, the Bundesrat will retain a say in all issues that significantly affect the finances of the individual states. In addition, Germany's federal states will be given a clearer mandate in several key policy areas.
The federal states will have greater powers to enact legislation on education issues, and they will each have their own autonomous civil service.
The states will also be permitted to introduce variable pay levels for government-funded professions, such as teachers. That element of competition could lead to some regions claiming to offer a better standard of education than others - with a potentially positive knock-on effect for the local economy.
The original federal system set up after World War II was meant to devolve decision-making to the states, bringing an end to the massive concentration of power at the national level seen under the Nazis.
Under the new system, only 35 to 40 percent of draft laws will need the approval of both houses of parliament, as opposed to 60 percent currently.
The reform took years to hammer out because of a tug-of-war over sovereignty in matters ranging from education and the penitentiary system to shop opening hours and care for the sick and elderly.
In each of these fields, the federal government agreed to give up some of its powers in exchange for the weakened influence of the Bundesrat and greater influence over issues such as fighting terrorism.
The agreement was considered the first major test for the unity of Merkel's unwieldy "grand coalition" government grouping her Christian Union and the Social Democrats.
The next major challenge is an overhaul of the public health care system. Merkel hopes to announce the broad outlines of the reform after a late-night cabinet meeting Sunday.