Meredith also said on Wednesday that it was immediately laying off roughly 200 employees and that it would eliminate about 1,000 more positions over the next 10 months. The layoffs are part of the company’s plan to cut between $400 million and $500 million in costs over the next two years. The company has also said it planned to move some noneditorial Time Inc. functions to Des Moines, where Meredith is headquartered.

The decision to sell Time, Sports Illustrated, Fortune and Money was widely expected. Still, the sale of what were some of Time Inc.’s most celebrated titles further signals the decline of the magazine industry. Though it had once helped shape American culture, Time Inc. has not just been swallowed up; it will soon be spit out in pieces.

Mr. Harty said that multiple parties — the majority of which he called “nontraditional wealthy individuals” — had expressed interest in buying the magazines. He said that he expected to announce deals by the end of June.

Meredith’s deal for Time Inc. was made possible by a $650 million infusion from Koch Equity Development, the private equity arm of the billionaire brothers Charles G. and David H. Koch. The brothers, Mr. Harty said, “have expressed no interest” in acquiring any of the four titles. He also said the company did not plan to sell the titles to another possible suitor: David J. Pecker, the chief executive of American Media Inc., who is close with President Trump.

Like many other magazines, Time, Sports Illustrated, Fortune and Money have battled vanishing advertising revenue and declining circulation. Sports Illustrated, once published weekly, has been reduced to every two weeks.