The lower house voted 428-162, with three abstentions, in favor of the plan, giving it the two-thirds majority that was required because it alters the constitution.
Officials have said the plan would cut the proportion of bills that need state approval from around 60 percent now to 30-40 percent. However, all bills that require financial outlay by state governments will require their approval.
The package also is aimed at clarifying which level of government is responsible for what areas of policy.
Still, recent weeks saw tensions between Merkel's conservatives and their center-left coalition partners, the Social Democrats, over details of the package.
The support of most Social Democrats was secured only after a compromise that gave the federal government more influence over education policy, which is largely a matter for state authorities.
Germany has long struggled to agree on reform of its cumbersome federal system.
The United States has imposed new sanctions against the Nord Stream 2 gas pipeline project, which still remains under construction