WASHINGTON—The U.S. Supreme Court on Tuesday said bankruptcy judges have the power to make final judgments in certain legal disputes—a decision that bolsters the power of U.S. Bankruptcy Court system.

In Wellness International Network Ltd. v. Sharif, the high court reversed an appellate court decision finding that the bankruptcy court didn’t have the constitutional authority to decide whether certain property belonged to the bankruptcy estate because the dispute also involved state laws.

The 6-3 ruling decided the country’s roughly 1,000 bankruptcy judges can make final decisions on legal disputes that arise in bankruptcy cases if all involved parties consent. Under a previous ruling, those disputes would have to be decided by a more powerful federal judge.

“Adjudication based on litigant consent has been a consistent feature of the federal court system since its inception,” Justice Sonia Sotomayor, writing for the court, said in 19-page ruling. “Reaffirming that unremarkable fact, we are confident, poses no great threat to anyone’s birthrights, constitutional or otherwise.”

After Richard Sharif filed for bankruptcy, Wellness International Network—a company to which Mr. Sharif owed half a million dollars—sued the Chicago man in bankruptcy court, claiming assets in a family trust tied to Mr. Sharif should be used to pay his debts.