The president is expected to take a break from his summer holiday to make the announcement.
Mr Bernanke has been praised for taking action to bail out failing banks, which Mr Obama believes has limited the effects of the economic crisis.
Mr Bernanke's four-year tenure comes up for renewal in January.
In remarks prepared for the announcement, Mr Obama said Mr Bernanke had helped prevent a repeat of the Great Depression.
"Ben approached a financial system on the verge of collapse with calm and wisdom, with bold action and outside-the-box thinking that has helped put the brakes on our economic free-fall," the president is expected to say.
"Our auto industry is showing signs of life. Business investment is showing signs of stabilizing. Our housing market and credit markets have been saved from collapse.
"Taken together, all of these steps have brought our economy back from the brink. They are steps that are working," he will say.
Future speculation
The Fed, along with the US Treasury, organised the $700bn (£496bn) bank bail-out plan in October 2008, and has since spent an additional $3 trillion propping up the credit markets and trying to boost the economy.
There had been speculation that Mr Bernanke would be replaced, perhaps by Larry Summers, who is the White House chief economic adviser.
But that would have gone down very badly with the financial markets, who see Mr Bernanke as the person who almost single-handedly staved off a meltdown, says the BBC's Greg Wood in Washington.
Mr Bernanke was named as Federal Reserve chairman by Mr Obama's predecessor, George W Bush, in 2005.
