A year ago, Chris Hughes, owner of the New Republic, vowed to continue his fight to transform the century-old magazine into a more digitally-focused media operation, despite a mass walkout by staffers who bristled at his efforts. On Monday, he said he was done.

The 32-year-old Mr. Hughes announced that he is putting the magazine up for sale. He admitted he had underestimated “the difficulty of transitioning an old and traditional institution into a digital media company in today’s quickly evolving climate.”

“After investing a great deal of time, energy, and over $20 million, I have come to the conclusion that it is time for new leadership and vision at The New Republic,” he wrote in a memo to staff.

The admission of defeat marked a sharp reversal from 2012 when the Facebook co-founder purchased a majority stake in the struggling magazine and expressed high hopes that the fast-evolving digital landscape had created great opportunities to “reinvigorate” the brand.

A Harvard roommate of Facebook founder Mark Zuckerberg, Mr. Hughes was in on the ground floor when the social media giant was created in 2004.

He left Facebook in 2007 to join President Barack Obama’s election campaign. According to Forbes, Mr. Hughes has a net worth of $450 million.

But the clash of cultures between Mr. Hughes’ Silicon Valley management style and the sensibilities of a traditional journalistic institution proved to be too much.

More than two dozen staffers and high-profile contributors walked away in December 2014, when a new CEO, Guy Vidra, announced plans to restructure the newsroom into a “vertically integrated digital media company.”

At the time, former Editor in Chief Franklin Foer said he was departing because his vision for the future of the publication was at odds with that of Mr. Hughes. He was replaced by Gabriel Snyder.

The magazine—a leading liberal voice in Washington, D.C., that used to promote itself as “the in-flight magazine of Air Force One” during the Clinton administration—cut the number of issues to 10 a year from 20 and moved its headquarters to New York.

From the Archives A Facebook co-founder takes a stake in “The New Republic.” Can new media save old media? MarketWatch columnist Jon Friedman weighs in on Mean Street. Photo: Agence France-Presse/Getty Images. (Originally published March 9, 2012)

The acrimonious fallout from the mass exodus—which triggered numerous critical broadsides against Mr. Hughes penned by the magazine’s long roster of notable alumni—proved to be difficult to overcome.

Web traffic declined by more than 50% following the tumult, according to comScore Inc., and hasn’t risen much in the past year.

In November, the site attracted 2.3 million unique visitors, down 38% from the same month a year earlier.

“Our disagreement didn’t help our ability to make The New Republic viable today, but it also did not spell our demise,” Mr. Hughes said. “Even though our search for a workable business model has come up short, we have shown that digital journalism isn’t at odds with quality and depth.”

In the memo, Mr. Hughes said finding a sustainable business model for the magazine had proven elusive.

“The New York Times, The Atlantic, and other traditional outlets seem to have found business models that work for them. I hope that this institution will one day be part of that list. To get there, The New Republic needs a new vision that only a new owner can bring,” he said.

A person familiar with the matter said Mr. Hughes had already begun preliminary talks with a variety of potential buyers, including larger media companies and digital startups.

One scenario being explored would be to sell the magazine to a philanthropist who would transform it into a nonprofit.

In a meeting with staff Monday, Mr. Hughes said he had no intention of laying anyone off and said business would proceed as normal until a new owner was found.

Mr. Foer—whose departure, in part, triggered the staff exodus a year ago—warned against interpreting Mr. Hughes’ move to sell as a sign that the magazine couldn't survive.

“The New Republic has spent 100 years cheating death. There have been plenty of times in the past when it appeared doomed, then somehow skated to safety. Maybe it will again,” he said in an email. “There are still good stewards in the world and there are ideas-driven magazines that make a difference.”

Write to Lukas I. Alpert at lukas.alpert@wsj.com