Fischer will retire from the Board of Governors by October 13 for "personal reasons", leaving his leadership post one year early and cutting his general term with the Fed two years short.
In a letter of resignation, Fischer said he was stepping down for unspecified "personal reasons" and cited the central bank's work to stabilize the United States financial system following the 2008 global financial crisis.
"The combination of his encyclopaedic knowledge of economics, outstanding judgment, quiet leadership and his perennial good humour has helped policymakers around the world to navigate one of the most challenging periods in the global economy".
Yellen's term as Fed chair ends in February.
In a note to clients on Wednesday, Paul Ashworth, chief U.S. economist at Capital Economics, wrote that Fischer's resignation "presumably lowers the odds of [Yellen] being nominated for a second term [as Fed Chair]".
Last month, Yellen spoke at the annual Jackson Hole Symposium, the year's top meeting of central bankers and economists from around the world, and gave an ardent defense of the USA government and the Fed's regulatory response to the financial crisis.
"Stan's keen insights, grounded in a lifetime of exemplary scholarship and public service, contributed invaluably to our monetary policy deliberations", Yellen said in Wednesday's statement.
Three spots on the seven-member board were already vacant. His resignation creates yet another opening for Trump to fill at a critical time for the Fed. I'm personally grateful for his friendship and his service.
Fischer, who was born in Zambia and educated in London, was nominated to the Fed by President Barack Obama after serving as the governor of the Bank of Israel from 2005 to 2013. Trump's first Fed nominee, Randal Quarles as vice chairman of banking supervision, is expected to be approved by the Senate Banking Committee on Thursday, and he is likely to clear the full Senate soon thereafter.