Obama also is nominating Lael Brainard as a Fed governor. Brainard served as the undersecretary for international affairs at Treasury during Obama's first term. She left the administration recently. He also is renominating Jerome Powell to the Fed for a second term.
All three nominations must be confirmed by the Senate.
"These three distinguished individuals have the proven experience, judgment and deep knowledge of the financial system to serve at the Federal Reserve during this important time for our economy," Obama said in a statement.
The selections were largely expected and did little to change economists' outlook for Fed policy this year. All three will likely support Yellen's approach to fighting high unemployment as long as inflation stays low. And all three are likely to back plans to gradually withdraw some of that support, if the economy continues to show improvement.
In December, the Fed said it would start reducing its bond purchases from $85 billion a month to $75 billion a month. Further "measured steps" are expected this year. The bond purchases are designed to lower interest rates to spur borrowing and spending.
In selecting Fischer, Obama is tapping someone with extensive experience in global economics. Fischer served as chief economist at the World Bank, deputy managing director of the International Monetary Fund, and head of the Bank of Israel from 2005 until 2013.
During his time at the IMF, Fischer dealt with a number of countries in financial crises. That included the 1997-98 Asian currency crisis, which forced a number of nations to seek support from the IMF to stabilize their currencies and emerge from deep recessions.
David Jones, chief economist at DMJ Advisors and the author of several books on the Fed, said Fischer had an excellent reputation in the field of monetary policy and would bring expertise in global economics.
"The White House has reached out to someone who has a wealth of not only theoretical experience but practical experience in monetary policy," Jones said.
Economists said they did not expect Fischer, 70, to dissent from the activist approach to Fed policy that Bernanke and Yellen have supported. That effort has kept interest rates low in an effort to stimulate growth and fight high unemployment since the Great Recession.
Critics say the central bank's policies, which also include massive bond purchases, could trigger unwanted inflation down the road. They also warn of a potential buildup in asset bubbles, which could destabilize financial markets.
During his time as head of Israel's central bank, Fischer earned praise for his handling of Israel's economy in the aftermath of the 2008 financial crisis.
Sung Won Sohn, an economics professor at the Martin Smith School of Business at California State University, said that Fischer's selection to help lead a second central bank may be part of a growing global trend. Britain last year tapped Mark Carney to lead the Bank of England after he had been head of the Bank of Canada.
"I think we are going to see more and more such moves," Sohn said. "Because of globalization, the world economy is now very interconnected."
Powell, a Republican, has been on the Fed board since 2012. He had been a partner at The Carlyle Group, a Washington-based investment firm from 1997 to 2005. He also served as a top official in the Treasury Department during the administration of President George H.W. Bush.