"In our opinion, she is the best possible leader for the Federal Reserve Board at this critical time in our nation's history," the letter said.
"Her knowledge of how the Fed sets policy, her understanding of the relationship between monetary policy and economic growth, and her ability to see and propose solutions to emerging economic problems is second to none," it said.
Among those signing the letter are Nobel Prize winner Joseph Stiglitz, former Fed governors Alan Blinder and Alice Rivlin, and two prominent former Yellen colleagues at the University of California-Berkeley, Christina Romer and Laura D'Andrea Tyson.
The letter, which still is adding names, comes as supporters of Yellen, the Fed's vice chair, and former Treasury Secretary Lawrence Summers are locked in an unprecedented public campaign to influence Obama's decision on who will replace Ben Bernanke.
Bernanke's second four-year term expires in January. Obama has said he would nominate a replacement this fall.
Although Yellen has been a staunch Bernanke ally and the Fed's No. 2 official, she has been viewed recently as the underdog because of Summers' ties to the White House. He was Obama's top economic advisor in 2009-2010, and some of his key allies remain at high levels of the administration.
Yellen's supporters have been more public in pressing their case.
The economists' letter was organized by Joyce Jacobsen, the dean of social sciences at Wesleyan University, and Heidi Hartmann, president of the Institute for Women's Policy Research, a Washington think tank.
Hartmann said she felt that Summers was getting more attention in the media recently and wanted to try to turn the focus back on Yellen.
"I felt that Yellen's qualifications were not getting the attention they deserved," she said.
About 250 economists signed the letter in the first 24 hours after it was posted Sunday night. Hartmann said organizers would continue adding names to the letter until Tuesday, when they planned to deliver it to the White House.
The letter cites three reasons Yellen would be the best choice to replace Bernanke.
As president of the Federal Reserve Bank of San Francisco in 2005, Yellen "warned of an impending real estate meltdown as asset prices rose unrealistically," the letter said. Two years later, Yellen was one of the first members of the Fed to warn a major recession could be coming.
The letter said Yellen has the ability to work "through cooperation and consensus" - a thinly veiled swipe at Summers, who has a reputation for being domineering and difficult to work with.
And Yellen is committed to lowering the still-high unemployment rate, the letter said.
Hartmann works to get more women in top economic positions, but the letter does not argue that Obama should pick Yellen because she would be the first woman to lead the Fed.
Hartmann said supporters hoped to offset some of the unfair criticisms of Yellen that smacked of sexism, such as she wouldn't handle a crisis as well as Summers.
"Her gender should not be a negative in considering her," Hartmann said. "She has so many qualifications, she's so skilled, she's not thought to be weak, she's not thought to be soft. The fact that that is coming out is a reflection of gender bias."