The board of Yahoo, the faded Web pioneer, agreed on Sunday to buy the popular blogging service Tumblr for about $1.1 billion in cash, people with direct knowledge of the matter said, a signal of how the company plans to reposition itself as the technology industry makes a headlong rush into social media.

The deal, which is expected to be announced as soon as Monday, would be the largest acquisition of a social networking company in years, surpassing Facebook’s $1 billion purchase of Instagram last year.

For Yahoo and its chief executive, Marissa Mayer, buying Tumblr would be a bold move as she tries to breathe new life into the company. The deal, the seventh since Ms. Mayer defected from Google last summer to take over the company, would be her biggest yet. It is meant to give her company more appeal to young people, and to make up for years of missing out on the revolutions in social networking and mobile devices. Tumblr has over 108 million blogs, with many highly active users.

Yet even with all those users, a basic question about Tumblr and other social media sites remains open: Can they make money?

Founded six years ago, Tumblr has attracted a loyal following and raised millions from big-name investors. Still, it has not proved that it can be profitable, nor that it can succeed on mobile devices, which are becoming the gateway to the Internet. Even Facebook faces continued pressure from investors to show it can increase its profits and adapt to the mobile world.

“The challenge has always been, how do you monetize eyeballs?” said Charlene Li, the founder of the Altimeter Group, a consulting firm. “Services like Instagram and Facebook always focus on the user experience first. Once that loyalty is there, they figure out how to carefully, ideally, make money on it.”

A Yahoo spokeswoman declined to comment. A representative for Tumblr did not respond to requests for comment.

If the deal is approved, Ms. Mayer will face the challenge of successfully managing the takeover, given Yahoo’s notorious reputation for paying big money for start-ups and then letting the prizes wither. Previous acquisitions by Yahoo, like the purchase of Flickr for $35 million and a $3.6 billion deal for GeoCities, an early pioneer in social networking, have been either shut down or neglected within the company.

Because of this, Ms. Mayer will face pressure to keep Tumblr’s staff, led by its founder, the 26-year-old David Karp, who dropped out of high school as a 15-year-old programmer. It is unclear whether all of Tumblr’s 175 employees, based in New York City, will move over to Yahoo.