The subpoenas, issued in April by the House Financial Services and Intelligence Committees, sought nearly a decade’s worth of tax returns and other financial documents that the banks obtained from Mr. Trump, his family and his companies. The subpoenas also demanded information about any suspicious activities that Deutsche Bank detected in Mr. Trump’s accounts.

Investigators for the two committees are hoping the materials will shed light on any links Mr. Trump has had to foreign governments and whether he or his companies were involved in any illegal activity, such as money laundering for people overseas.

The committees have also said the information is important to their attempts to write legislation. Mr. Trump’s lawyers have argued that the subpoenas served no legitimate legislative purpose and were overly broad.

“This ruling ensures that a significant amount of the materials sought by our committees will continue to be produced,” said a statement by the Financial Services chairwoman and the Intelligence chairman, Representatives Maxine Waters and Adam B. Schiff, both of California.

The ruling by the appellate panel, with two judges appointed by President George W. Bush and one by President Jimmy Carter, contained a caveat: The lower court must consider whether and how the banks disclose a limited set of sensitive personal information that would have no bearing on the government investigations. Such information could include checks that were written by Mr. Trump or his companies to cover employees’ medical expenses.

But, the court ruled, the presumption should be in favor of handing over more documents, not fewer. “Many documents facially appearing to reflect normal business dealings will therefore warrant disclosure for examination and analysis by skilled investigators assisting the committees to determine the effectiveness of current regulation and the possible need for improved legislation,” the court wrote.

The ruling concluded: “The committees’ interests in pursuing their constitutional legislative function is a far more significant public interest than whatever public interest inheres in avoiding the risk of a chief executive’s distraction arising from disclosure of documents reflecting his private financial transactions.”