President Trump’s former national security adviser, Mike Flynn, was paid tens of thousands of dollars by Russian companies shortly before he became a formal adviser to the then-candidate, according to documents obtained by a congressional oversight committee that revealed business interests that hadn’t been previously known.

Mr. Flynn was paid $11,250 each by a Russian air cargo company that had been suspended as a vendor to the United Nations following a corruption scandal, and by a Russian cybersecurity company that was...