The boards of Sprint Corp. and T-Mobile US Inc. struck an all-stock $26 billion merger that, if allowed by antitrust enforcers, would leave the U.S. wireless market dominated by three national players.

It is the third time in recent years that the two rivals have attempted the combination.

New technology, stiff competition from wireless rivals and an aging cellphone sector keep driving Sprint and T-Mobile into each other’s arms. Both companies hope to squeeze billions in savings by uniting operations despite their owners’ different management styles and a tough regulatory environment.

The all-stock deal would combine Sprint, which has a market value of $26 billion, with T-Mobile, which has a market value of $55 billion, based on Friday’s closing prices. The two companies also have about $60 billion of combined debt.

Under the terms of the deal, T-Mobile will exchange 9.75 Sprint shares for each T-Mobile share. T-Mobile parent Deutsche Telekom will own 42% of the combined company and Sprint parent SoftBank Group will own 27%. The remaining 31% will be held by the public.

Deutsche Telekom would also control voting rights over 69% of the new company and appoint nine of its 14 directors. The companies said they hope to close the deal in the first half of 2019.

Joining forces would create a wireless provider with nearly 100 million cellphone customers, second only in the U.S. to Verizon Communications Inc. The combined company, which would be called T-Mobile, would be run by T-Mobile CEO John Legere. .

The companies will still face an uphill battle in Washington. The Republican administration hasn’t been consistently receptive to big corporate mergers. The Justice Department sued AT&T Inc. in November to block its $85 billion takeover of Time Warner Inc., and lawyers for the two sides are making closing arguments on Monday.

In a reflection of the risk that authorities would block an attempt at combining the nation’s third- and fourth-largest wireless carriers, the Sprint-T-Mobile deal isn’t expected to include a break-up fee that one side would owe should regulators block a proposed tie-up, the people familiar with the matter said.

The government also has a past victory under its belt: It forced AT&T Inc. and T-Mobile to abandon a planned tie-up in 2011.

In 2014, the then head of the Federal Communications Commission made clear that having four national providers was necessary to ensure competition and lower prices for consumers. That forced Sprint and T-Mobile to abandon their plans to combine. The current FCC chairman, Republican Ajit Pai, hasn’t drawn the same line about the number of national providers.

“This isn’t a case of going from 4 to 3 wireless companies — there are now at least 7 or 8 big competitors in this converging market,” Mr. Legere said on Sunday. The companies also vowed to boost hiring and spending in the U.S. after the transaction.

Sprint and T-Mobile executives could make the case that times have changed. Investments in 5G infrastructure could blur the lines between cellphone provider, cable company and technology firm. Even using current technologies, Comcast Corp. has rolled out low-cost wireless service to its cable customers that rides on Verizon’s network.

Dish Network Corp., led by its chairman Charlie Ergen, meanwhile is building a bare-bones wireless network that could be used to link autonomous cars, drones and other machines aside from cellphones. Companies could use that project to argue there are more than four nationwide wireless companies, though it would be a harder sell if Dish avoids directly competing with Sprint and T-Mobile.

“Charlie alone can change the prospects of this deal,” said Blair Levin, a regulatory analyst for New Street Research LLC.

Last year, Sprint and T-Mobile discussed a deal but the talks collapsed in November after they failed to agree on who would control the combined company, people familiar with the matter said. Japanese technology giant SoftBank controls 83% of Sprint. Germany’s Deutsche Telekom owns 62% of T-Mobile.

SoftBank founder Masayoshi Son, whose firm took control of Sprint for $22 billion in 2013, was reluctant to give up control of Sprint last year. One person close to Mr. Son said the pressure on Sprint to roll out 5G technology made him more amenable to relinquishing some control.

Mr. Son will join the board of the combined company but the board’s chairman will be Deutsche Telekom CEO Tim Höttges. Sprint CEO Marcelo Claure will also join the combined board, the companies said.

Shares of Sprint have gained 25%, closing Friday at $6.50, since The Wall Street Journal reported on April 10 that the two sides had rekindled talks.

The companies pledged Sunday to invest up to $40 billion on its network and business in the first three years after the deal closes. But the companies, which would employ about 200,000 people and own thousands of retail stores, will also be looking to cut costs. On Sunday, they projected savings totalling $6 billion in annual costs.

Wireless executives have long complained there are fewer ways to grow profits now that nearly every American adult — and many of their children — owns a smartphone. They hold onto those devices for longer, cutting into equipment sales. All four top carriers now offer plans that promise unlimited data, making it harder for them to show they’re different from their rivals.

Even T-Mobile, which adds millions of customers each year mostly at its rivals’ expense, has showed signs that growth is cooling. The company predicted it would add 2 million to 3 million subscribers with monthly contracts this year, fewer than in 2017. Such so-called postpaid subscribers are lucrative because they tend to spend more each month and switch less often than people on prepaid plans.

Meanwhile, network engineers say the next-generation 5G standards could allow wireless companies to serve huge new markets, from home internet service still dominated by cable companies to autonomous cars just now being developed.

But rolling out 5G services will require heavy investment in cellular spectrum and installing hundreds of thousands of antennas around the country, which gave new impetus to Sprint and T-Mobile executives to join forces.

AT&T said it will devote at least $23 billion to capital spending this year, excluding some investments in a new public-safety network. Verizon said it plans to spend at least $17 billion on capital expenditures in 2018. Both budgets are well ahead of Sprint and T-Mobile, which each spend under $10 billion a year on construction, electronics and the like.

Left alone, the spending gap will only widen as companies rush to install 5G equipment. “You can’t win a race by having half the horses,” said Roger Entner, an analyst for telecom consultant Recon Analytics Inc.

Winning the race wouldn’t come cheap. Consulting firm Accenture estimates that U.S. telecom companies together could invest $275 billion over the next seven years to deploy the next-generation wireless technology.

No wireless company has much time to decide. The FCC will launch two new auctions for wireless spectrum licenses at the end of this year, forcing the companies to decide how they want to spend billions of dollars. Federal rules also require bidders to halt talks before the auctions to avoid coordinated bidding.