The administration also reached out to former Treasury Secretary Timothy Geithner early in the process. Geithner said he was not interested in being considered.
Obama is expected to announce a nominee for the Fed chairmanship as early as this month. Bernanke's term ends Jan. 31, 2014.
Some economists said Sunday that they think Summers' exit significantly boosts the likelihood of a Yellen nomination.
"The odds that the president will nominate Janet Yellen are now much higher," said Mark Zandi, chief economist at Moody's Analytics.
Still, Zandi added, "There is a chance that there is some dark horse candidate, possibly Tim Geithner."
David Jones, chief economist at DMJ Advisors and the author of several books on the Fed, said he saw Yellen's selection as a virtual certainty.
"There is a strong view that making a woman Fed chair is an important step," Jones said. "There is no question that her experience qualifies her for the role."
Summers and his allies had been engaged in an unusually public contest with Yellen supporters, with each side lobbying the administration.
An openly waged succession battle is something that the Fed, which will turn 100 in December, has never before witnessed. The selection of a chairman has typically been a matter handled privately by a president and his senior advisers.
In a statement Sunday, Obama said he had accepted Summers' decision.
"Larry was a critical member of my team as we faced down the worst economic crisis since the Great Depression, and it was in no small part because of his expertise, wisdom and leadership that we wrestled the economy back to growth and made the kind of progress we are seeing today," Obama said.
Yet Summers faced strenuous opposition from some Democrats, including some on the Senate Banking Committee. Summers alluded to that opposition in a letter he sent Sunday to Obama to formally withdraw from consideration.
"I have reluctantly concluded that any possible confirmation process for me would be acrimonious and would not serve the interests of the Federal Reserve, the administration or ultimately, the interests of the nation's ongoing economic recovery," Summers wrote.
Summers' ascent to the top of the list to succeed Bernanke rankled both opponents of the president as well as some liberal supporters. He has alienated colleagues in the past with a brusque and at times domineering style. Unlike Bernanke, he's not been known as a consensus-builder one reason some critics had opposed his nomination.
He was also seen as having been too cozy with Wall Street. And Summers was roundly criticized for questioning women's innate skills in math and science comments that contributed to his forced resignation as Harvard's president in 2006.
Shaunna Thomas, co-founder of the women's rights group UltraViolet, welcomed Summers' withdrawal, saying she hopes it serves as "a reminder to all that sexism has no place anywhere in society and certainly not in the highest levels of our government."
Thomas called on Obama to nominate Yellen, 67, who has been closely aligned with Bernanke and has helped devise the Fed's low-interest rates policies.
Since joining the Fed's board as vice chair in 2010, Yellen has supported Bernanke's use of not only the Fed's traditional tool of short-term interest rates but also non-traditional tools designed to help the economy. These include bond purchases and guidance to investors about the likely direction of rates.
As early as this week, the Fed is expected to scale back its $85 billion-a-month in Treasury and mortgage bond purchases. Those purchases have been designed to keep long-term loan rates low to get people to borrow and spend and invest in the stock market.
The low rates are credited with helping fuel a housing comeback, support economic growth, drive stocks to record highs and restore the wealth of many Americans.
Yellen has long been considered a top candidate for the chairmanship in part because of her expertise as an economist, her background as a top bank regulator and her experience as vice chair. Last week, more than 350 economists signed a letter to Obama calling on him to nominate her. The letter was designed to draw attention back to Yellen amid signs that Obama was leaning toward Summers.
The letter, whose signers include economists with ties to Obama, credited Yellen for prescience in warning in 2005 about the impending mortgage meltdown, for her consensus style of leadership and for her commitment to job growth.
Liberal critics of Summers had focused in particular on the role he played in deregulating parts of the financial industry during the Clinton administration.
More than 20 Democratic senators this summer signed a letter to Obama expressing support for Yellen. The letter was circulated by Sen. Sherrod Brown of Ohio, a member of the Banking Committee.
Last week, another committee Democrat, Jon Tester announced he would oppose Summers. Aides to Brown and to Sen. Jeff Merkley, also on the committee, indicated that their bosses intended to oppose Summers, too.
That meant Summers would have to win support from Republicans on the committee, a tough challenge.
Still, a Yellen nomination would likely face resistance from many Republicans. Critics argue that the Fed's low-rate policies have raised the risk of high inflation and dangerous bubbles in assets like real estate and stocks. Yellen is seen as a leading architect of those policies.
Obama had vigorously defended Summers in recent weeks, both in public comments and in closed-door meetings with lawmakers.
"I will always be grateful to Larry for his tireless work and service on behalf of his country, and I look forward to continuing to seek his guidance and counsel in the future," Obama said Sunday.
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Associated Press writer Jim Kuhnhenn contributed to this report.
