The leaders of both companies are determined to close a deal, if only because their prospects going it alone grow dimmer by the year.

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 see T-Mobile, which has a market value of $55 billion, take control of Sprint, which has a market value of $26 billion, both based on Friday’s closing prices. The two companies also have about $60 billion of combined net debt.

The combined company, which would be called T-Mobile, would be run by T-Mobile CEO John Legere.

Under the deal, T-Mobile will exchange 9.75 Sprint shares for each T-Mobile share. T-Mobile parent Deutsche Telekom AG 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 in the same class as Verizon Communications Inc., which reported about 116 million wireless customers in the U.S. at the end of 2017, and close to AT&T Inc., which said it had 93 million wireless customers. T-Mobile and Sprint had roughly 59 million and 41 million, respectively, at the end of last year. The figures exclude some connected devices and wholesale agreements with other carriers riding atop the major carriers’ networks.

The companies will face regulatory challenges in Washington. 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 will block combination, the T-Mobile-Sprint deal doesn’t include a break-up fee that one side would owe should regulators block a tie-up, the people familiar with the matter said.

The government also has a 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.

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.

“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.

The companies said they plan to add to their combined headcount of roughly 80,000 full-time U.S. employees once the deal closes.

“This is one of those few mergers that are actually going to be net job positive from the get-go,” Sprint CEO Marcelo Claure said. “We’re going to go build an amazing network that is good for the economy.”

Teaming up would allow the companies to decommission about 35,000 cellular transmission sites, cutting the cost of rent and maintenance.

The two companies have already signed a wireless roaming agreement to set themselves up to merge infrastructure. T-Mobile technology chief Neville Ray said it could take two or three years to move all customers onto the new system.

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 with an eye toward combining it with T-Mobile, 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. Mr. Claure will also join the combined board, the companies said.

The companies said they would keep T-Mobile’s base in Bellevue, Wash. and use Sprint’s Overland Park, Kansas, offices as “second headquarters.”

The companies pledged Sunday to invest up to $40 billion on the network and business in the first three years after the deal closes. But the companies, which own thousands of retail stores, will also be looking to cut costs. On Sunday, they projected savings totaling $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.

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.

Without a merger, the spending gap with Verizon and AT&T 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.

Write to Drew FitzGerald at andrew.fitzgerald@wsj.com, Dana Cimilluca at dana.cimilluca@wsj.com and Dana Mattioli at dana.mattioli@wsj.com