If the sale has come as a relief to Tronc executives and Times journalists alike, it leaves Dr. Soon-Shiong with the unenviable task of owning a major daily paper at a time when the newspaper business is increasingly reliant on the support of deep-pocketed patrons. With the purchase, he would become the latest wealthy businessman to take ownership of a struggling newspaper in a big city, following Jeff Bezos with The Washington Post, John Henry with The Boston Globe and Sheldon Adelson with The Las Vegas Review-Journal.

“We look forward to continuing the great tradition of award-winning journalism carried out by the reporters and editors of The Los Angeles Times, The San Diego Union-Tribune and the other California News Group titles,” Dr. Soon-Shiong said in a statement on Wednesday.

Dr. Soon-Shiong — who grew up the son of Chinese immigrants in apartheid South Africa and largely made his fortune selling generic medicines and developing a new cancer drug — became a major Tronc shareholder and vice chairman two years ago as part of the company’s effort to stave off a takeover attempt by Gannett, the publisher of USA Today. In a 2016 interview with The New York Times, Dr. Soon-Shiong said he considered newspapers a “public trust.” But his relationship with Mr. Ferro soon deteriorated, leading to Dr. Soon-Shiong’s removal from Tronc’s board last year.

He takes over one of the most decorated newspapers in the country, with 44 Pulitzer Prizes. But The Times has struggled in recent years as newspapers across the country have lost heft and cultural importance.

Last decade, the paper weathered the cost-slashing reign of Samuel Zell, who took Tribune Company into bankruptcy. In 2014, after emerging from bankruptcy proceedings, the company spun off its newspaper division, creating Tribune Publishing.

When Mr. Ferro, a Chicago entrepreneur and a former owner of The Chicago Sun-Times, took a major stake in Tribune Publishing in 2016, he introduced grand plans that included the use of artificial intelligence. He also rebranded the company as Tronc, which stood for Tribune online content, a name that has gotten laughs in newsrooms ever since. (The brand name appears formally as tronc, in lowercase letters, in company statements.)

The Times, with bureaus in cities including Lagos and Rio de Janeiro, was to be the linchpin of Tronc’s global ambitions. But over the past year the paper proved too much to handle. In August, Tronc ousted top members of the Times management team, including Davan Maharaj, its editor and publisher, and installed the former Yahoo executive Ross Levisohn as publisher. Lewis D’Vorkin, a former chief product officer at Forbes, later joined the paper as editor in chief.