He previously served as governor of the Bank of Israel from 2005 through 2013.
In view of the replacement of USA economic leadership planned by President Donald Trump, however, the likelihood that Fischer would be appointed was brought into question.
Appointed to the board for an unexpired term finalising on 31 January, 2020, his term as vice chairman was due to expire on 12 June 2018.
In his letter to the president, Fischer said "It has been a great privilege to serve on the Federal Reserve Board and, most especially, to work alongside Chair [Janet] Yellen as well as many other dedicated and talented men and women throughout the Federal Reserve system".More news: Sitharaman new Defence Minister, Piyush gets Railways
"The strength of the financial system is absolutely essential to the ability of the economy to continue to grow at a reasonable rate, and taking actions which remove the changes that were made to strengthen the structure of the financial system is very unsafe", Fischer said in April.
Quarles's nomination is scheduled to be voted on by the Senate Banking Committee on Thursday.
Fischer's resignation from the Federal Reserve Board will be effective on or around October 13, according to a statement from the Fed.
"It would be easier to keep her around, " Swonk said.More news: Unexploded WW-II bomb found in Frankfurt, 65000 residents evacuated
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". "In a recent interview with the Financial Times, Fischer was highly critical of Republican efforts to loosen the post-crisis regulatory regime".
Reports earlier this year suggested that a leading candidate for one of the other vacant slots is Marvin Goodfriend, an economics professor at Carnegie Mellon University in Pittsburgh.
As for Yellen's replacement, NEC Cohn will likely take the Fed Chief job if he wants it and can, with Trump, trim the number of PhD economists in favor of more business executives like former Goldman Sachs President Cohn.More news: Cambodia arrests opposition leader for 'treason'