The central bank's staff suspected hackers or spies in many of the incidents, the records show.
The Fed's computer systems play a critical role in global banking and hold confidential information on discussions about monetary policy that drives financial markets.
The cybersecurity reports, obtained by Reuters through a Freedom of Information Act request, were heavily redacted by Fed officials to keep secret the central bank's security procedures.
The Fed declined to comment, and the redacted records do not say who hacked the bank's systems or whether they accessed sensitive information or stole money.
"Hacking is a major threat to the stability of the financial system. This data shows why," said James Lewis, a cybersecurity expert at the Centre for Strategic and International Studies, a Washington think tank. Lewis reviewed the files at the request of Reuters.