In an update posted to the central bank's website at 1545 BST, the central bank said that Fischer, aged 73, would be stepping down from the Board of Governors of the Federal Reserve System on or about 13 October.
The term of the current chair of the Fed, Janet Yellen, is due to end in February 2018.
At the same time, the Trump administration now has an unprecedented opportunity to reshape the Federal Reserve.
In July, he nominated investor Randal Quarles to fill one of the vacancies.
Last month in an interview, Trump said he was considering either re-nominating Yellen for a second term as Fed chair or replacing her.
"During my time on the Board, the economy has continued to strengthen, providing millions of additional jobs for working Americans", Fischer wrote in the letter.
The White House said it had no immediate comment on Fischer's departure or on the timing for filling his spot or other positions at the Fed.
"It has been an extraordinary privilege - and exceptionally good fortune - for me to have worked closely with Stan Fischer", Bank of England Governor Mark Carney said in a statement.
Reports have indicated that Yellen and Trump's chief economic advisor Gary Cohn, formerly the president and COO at Goldman Sachs (GS), are the top two candidates for the role.
With an academic approach to policymaking, born of professorship at the Massachusetts Institute of Technology and University of Chicago, Fischer had contributed a more moderate perspective on interest rate hikes and voted for the Federal Open Market Committee's monetary policy action. The Fed's rate-setting policy committee, which includes some of the regional reserve bank presidents, can also continue to meet. He was also the first deputy managing director of the International Monetary Fund from 1994 to 2001 and was the chief economist for the World Bank between 1988 and 1990.
He was Governor of the Bank of Israel between 2004 and 2013.