More recently, digital media companies have also started to struggle, leading many outlets to ponder joining with rivals to increase their chances of long-term survival. Venture capital-backed sites like BuzzFeed, Vice, Bustle, Refinery29 and Group Nine have sought mergers in the last year, arguing that scale and cost savings are crucial at a time when digital advertising, dominated by Google and Facebook, fails to pay the bills. More than 1,000 employees lost their jobs this year in layoffs at BuzzFeed, AOL, Yahoo, HuffPost and Vice Media.

Digital media companies with diverse revenue streams can still thrive. Mr. Bankoff reshaped Vox Media to rely less on digital advertising, and after expanding its video and podcast businesses, the company had a modest profit on $185 million in revenue last year.

Even with the addition of New York Media, Vox Media expects to remain profitable, Mr. Bankoff and Ms. Wasserstein said. Bolstered by its new acquisition, Vox Media expects to exceed $300 million in revenue by the end of 2020, according to two people familiar with the deal, putting it on a par, in terms of annual revenue, with BuzzFeed. (Mr. Bankoff and Ms. Wasserstein declined to comment on financial projections for the revamped Vox Media.)

“We see a lot of mergers that are done for the wrong reason: because one or two companies might be desperate, or for financial engineering,” Mr. Bankoff, known for his straightforward style, said. “We’ve been struck by the lackluster ambitions of a lot of the other tie-ups, and the lackluster rationales. What was important to us both was making sure that the market knew that this was something different.”

Vox Media got its start, in 2005, as SB Nation, a network of sports fan sites. Since Mr. Bankoff, a onetime executive at AOL, was hired in 2009 to lead the company, it has started new titles such as The Verge and Polygon, which cover tech and gaming, and acquired others. Those include Recode, founded by Kara Swisher (also an opinion writer for The New York Times) and Walt Mossberg, as well as Eater and Curbed.

Vox.com, founded in 2014 by Ms. Bell, Ezra Klein and Matthew Yglesias, is the general-interest flagship known for explanatory journalism. The site’s “explainers” have become a journalistic genre, with their guides to everything from nuclear-weapons deals to internet ephemera.

The company cut a production deal in May with the streaming service Hulu to create TV shows centered on food and family with David Chang and Chrissy Teigen. Vox Media also renewed a production agreement with Netflix for “Explained,” a series based on Vox’s specialty, and it has generated revenue by building its conference business and licensing its content management system, Chorus.