Yahoo Inc. has agreed to pay $1.1 billion for Tumblr, a six-year-old company with more than 100 million users but very little revenue, a deal that highlights the shifting balance of power in the technology business.

Veterans like Yahoo have shown they have staying power—and they have cash to spend. But companies like Yahoo's target, a blogging site, have something valuable as well: the rapt attention of fast-growing communities of users. That has pushed up the price tags as...