"Almost none of the decisions he or any of us made have been easy."
The US senate will next decide on whether to ratify Bernanke's appointment.
Bernanke has gained support, notably on Wall Street, for the unorthodox methods he used to prop up the ailing banking sector and reorient the financial industry.
However, he has also been criticised for the extent of the Fed's lending operations under his stewardship.
"The second four-year [term] of Bernanke [is] going to be defined as a success or failure on how he takes the money back, when he takes it back, and what happens when he does take it back"
Max Wolff, economics professor at New School University in New York
The balance sheet of the central bank now stands at more than $2 trillion - doubling in the last year - in part due to the loans it has granted to banks.
Max Wolff, a professor of economics at the New School University in New York, said: "The easy part of [Bernanke's] job was in flooding the world economy with lots and lots of extra dollars, lowering the interest rates on borrowed monies and making sure that there is a lot more money out there to borrow.
"Handing out the candy is always easier than taking it back. What the next few years will involve is the threat of serious inflation and unwinding a lot of these gigantic programmes that have flooded an additional several trillion dollars of new loanable funds into the market to lower interest rates, keep American banks, insurance companies and households solvent.
"The second four-year [term] of Bernanke [is] going to be defined as a success or failure on how he takes the money back, when he takes it back, and what happens when he does take it back."
After the announcement, Chris Dodd, the senate banking committee chairman, said in a statement that Bernanke would receive a "thorough and comprehensive confirmation hearing" for re-nomination.
"I still have serious concerns about the Federal Reserve's failure to protect consumers and I strongly believe these responsibilities should go to an independent consumer financial protection agency," he said.
But Dodd said Obama's decision was "probably the right choice".
Bernanke said on Tuesday that the Federal Reserve had been "bold or deliberate as circumstances have demanded".
"But our objective remains constant. To restore a more stable financial and economic environment in which opportunity can again flourish," he said.
Bernanke added that if he is confirmed by the senate, he will work to provide "a strong foundation for growth and stability" in the economy.
Tom Palley, an economist in Washington DC, told Al Jazeera that Bernanke's nomination was "sensible and pragmatic", but said that the role of the Fed needs greater examination.
"Let's face it, there are lots and lots of questions outstanding about the Federal Reserve, its policy before the crisis and also why it was slow to address the crisis.
"He has a tough job in front of him. But ... this re-nomination should be an occasion for introspection.
"Bernanke took some very good decisions late in October 2008. But we should be asking what went wrong in the Federal Reserve before then. His peer group has failed us."
Bernanke originally took the position of Federal Reserve chairman in 2005, after being selected by George Bush, the former president.