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Responding to a wave of consolidation in the telecommunications industry, the nation’s third- and fourth-largest wireless phone operators have agreed on the terms of a deal to join forces.

Sprint and T-Mobile have talked about a combination for years but continued to put it off, each preoccupied with other deals, and concerned about scrutiny from antitrust regulators.

But in recent days, the two sides have settled on the terms of a $32 billion deal that is likely to be announced this summer, people briefed on the matter said on Wednesday.

Under the terms of the deal, which are still preliminary, Sprint would acquire T-Mobile for about $40 a share in cash and stock, a 17 percent premium to Wednesday’s price.

Talks are incomplete and could still fall apart. But the agreement on terms represents a turning point in a relationship between two companies that have long contemplated a merger.

Sprint and T-Mobile have decided to press ahead now because their two main rivals, Verizon and AT&T, each with more than 100 million subscribers, continue to grow more formidable.

Verizon’s balance sheet is stronger, after agreeing to take full control of Verizon Wireless last year in a $130 billion deal with Vodafone. Verizon is the largest wireless operator in the country and also provides landlines, cable television and business services.

AT&T, the second-largest wireless provider, recently agreed to acquire DirecTV in a $49 billion deal, which would give it control of the country’s largest satellite television operator.

Meanwhile, the cable industry is also consolidating. Comcast and Time Warner Cable have agreed on a $45.2 billion deal that would create by far the largest cable television operator. The combined company would also have strong landline, Internet and business services offerings.

Together, these mergers and acquisitions by competitors of Sprint and T-Mobile have created a landscape that has increasingly marginalized the two smaller companies, which each have about 50 million subscribers and only provide wireless service.

Neither Sprint nor T-Mobile, on their own, would have the financial resources to compete against these larger players, nor the suite of offerings to attract customers who can get a whole host of services from other rivals. As a result, both sides believe that the only way to remain relevant is to combine.

Sprint and T-Mobile are both majority-owned by large, international telecommunications groups, which have their own agendas as well. T-Mobile is 67 percent owned by Deutsche Telekom of Germany. Last year, T-Mobile merged with MetroPCS, gaining a publicly traded stock that eased the path for a Sprint deal.

Deutsche Telekom has been looking to get out of its T-Mobile investment for years, and under the proposed deal with Sprint it would own just 20 percent of the combined firm, further reducing its United States exposure.

Sprint, meanwhile, is majority-owned by SoftBank, the Japanese group controlled by the billionaire Masayoshi Son. Mr. Son, known as Masa, an entrepreneur who has already reshaped Japan’s wireless industry, has made no secret of his ambitions to do the same thing in the United States. Taking control of Sprint last year was his first step, and at the time that deal was announced, he acknowledged his desire to acquire T-Mobile as well, giving him the scale he thinks he needs to compete with Verizon and AT&T.

“AT&T and Verizon dominate the industry’s Ebitda and capital investment,” said Walter Piecyk, an analyst at BTIG Research, referring to a common indicator of a company’s financial performance. “And Masa is making a credible case that they not only need scale to compete more effectively in the wireless industry but could also offer new and needed competition for wired broadband.”

Should it be announced this summer, a deal to combine Sprint and T-Mobile would surely face regulatory scrutiny. Antitrust officials at the Justice Department are already considering the implications of Comcast’s proposed acquisition of Time Warner Cable, and AT&T’s proposed deal for DirecTV. This would add a third megadeal to the mix, and the regulators could consider the merits of all the deals at once.

“Regulators have many deals in front of them and need to consider where the market will be five years from now and how to best stimulate competition, which not only means lower prices but also more investment,” Mr. Piecyk said.

AT&T tried to buy T-Mobile three years ago in a deal that would also have consolidated the industry. But regulators effectively killed the deal, contending it would have been bad for consumers because it would have reduced their choices.

Accounting for the regulatory uncertainty, the early terms of the deal include a breakup fee of more than $1 billion that Sprint would pay T-Mobile if the deal is not consummated.

Many hurdles to the deal remain, and any announcement is still a ways off. The two sides have not conducted due diligence on one another, drafted a definitive agreement or arranged financing. A deal could be announced in July, according to a person briefed on the process.

Additionally, by expanding so rapidly, Mr. Son of Japan will have created a company with a substantial amount of debt. Together, the two companies carried about $54 billion in long-term debt as of March 31, according to regulatory filings.

There is also the issue of T-Mobile’s brash chief executive, John J. Legere. Mr. Legere supports the merger, and could emerge as the leader of a combined company. Dan Hesse, Sprint’s chief executive, has previously signaled his willingness to step down.

Despite turning around T-Mobile, Mr. Legere has said publicly that his smaller company lacks the financial firepower to battle Verizon and AT&T over the long term.

“When you play this game over five years or so, there are capital requirements and there are multiple ways to continue to play aggressively and to close the gap on the big guys,” he said in a recent earnings call. “We’ve always said that we think, ultimately in the industry, it’s a consolidation game. That’s a matter of when and not if.”

Bloomberg and The Wall Street Journal earlier reported that the companies had agreed on deal terms.

Craig Moffett, the senior research analyst for MoffettNathanson, said that the timing of the potential takeover stems in part because Mr. Son is eager to use Sprint’s stock as deal currency while it remains relatively highly valued.

But Mr. Moffett cited the likelihood of strong opposition by the Justice Department’s antitrust division and the Federal Communications Commission in both private and public comments.

“I don’t think you can put more than a 10 percent chance of success for this deal,” he said.

Among the three proposed deals that the F.C.C. and the Justice Department will weigh, Mr. Moffett considers that the Comcast and AT&T proposals will be the ones to pass, since either approving all three or rejecting them all would be politically untenable. “They will have to find at least one acquisition to be the sacrificial lamb,” he said.

Combining Forces

T-Mobile’s planned merger with Sprint would be about the 18th largest deal in the industry since 1984.