Fischer's resignation will be effective on or around 13 October. He has been a member of the board since May 2014.
Janet Yellen, chair of the Fed, said: "Stan's keen insights, grounded in a lifetime of exemplary scholarship and public service, contributed invaluably to our monetary policy deliberations. He represented the board internationally with distinction and led our efforts to foster financial stability."
"I'm personally grateful for his friendship and his service. We will miss his wise counsel, good humour, and dry wit."
During his time on the board, Fischer served as chairman of the Committee on Financial Stability as well as the Committee on Economic and Financial Monitoring and Research.
Prior to his role at the Fed, Fischer worked as the governor of the Bank of Israel and as the vice chairman of Citigroup.
In a letter to President Donald Trump, Fischer said it was a privilege to serve the Federal Reserve board and to work alongside Yellen.
"During my time on the board, the economy has continued to strengthen, providing millions of additional jobs for working Americans," he said.
Informed by the lessons of the recent financial crisis, we have built upon earlier steps to make the financial system stronger and more resilient and better able to provide the credit so vital to the prosperity of our country's households and businesses.
Mark Carney, governor of the Bank of England, said Fischer's contributions would continue to be studied in the years ahead.
“The combination of his encyclopaedic knowledge of economics, outstanding judgement, 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.
"In the years ahead, students and practitioners of macroeconomic policy will continue to draw inspiration from Stan’s contributions at the Federal Reserve and the Bank of Israel, his earlier stellar career at the IMF [International Monetary Fund] and his many and varied academic contributions."