T-Mobile’s parent, Deutsche Telekom, will get a better exchange ratio in the all-stock deal.

Photo: Justin Sullivan/Getty Images

Sprint Corp. S -0.11% and T-Mobile TMUS -0.99% US Inc. have agreed on new terms for their merger, as the wireless carriers race to close the deal after overcoming a federal court challenge.

The parties will improve the exchange ratio in the all-stock deal for T-Mobile’s parent, Deutsche Telekom AG , the companies said in a written statement confirming an earlier Wall Street Journal report.

U.S. District Judge Victor Marrero last week allowed the deal to proceed by rejecting arguments from a group of state attorneys general seeking to block the merger as anticompetitive.

T-Mobile said after the court ruling that it was working to close the transaction as soon as April 1.

Originally, 9.75 Sprint shares were to be exchanged for each T-Mobile share. Under the revised deal, SoftBank Group Corp., which owns more than 80% of Sprint’s common stock, will exchange the equivalent of 11 of its shares for each T-Mobile share. Sprint’s other shareholders will continue to get the original exchange ratio.

Deutsche Telekom is to own about 43% of the combined company now, up from just below 42% when the deal was first announced nearly two years ago, the companies said. SoftBank’s percentage will drop to approximately 24% from 27%. The remaining 33% is to be held by the public, up from 31%.

To effect the changes, SoftBank has agreed to surrender 48.8 million T-Mobile shares to the new company, to be called T-Mobile. Those shares could be reissued to SoftBank if T-Mobile’s stock price reaches certain milestones beginning two years after the deal closes.

The original merger agreement allowed either party to walk away after Nov. 1, 2019, without paying a penalty. Both companies stuck with the deal over the following months, however, as they defended it in federal court. They argued the merger would create a more efficient network that would offset any harm to competition.

Given the downward slide of Sprint’s shares amid continued customer defections since the tie-up was announced—as T-Mobile’s growing customer base pushed up its stock—Deutsche Telekom was expected to push for an altered exchange ratio and a larger share of the new T-Mobile.

When the deal was announced, Sprint shares were trading around $6.50. Before the court ruling Feb. 11, Sprint’s share price had sunk to $4.80. It has since jumped above $9. Sprint shares closed nearly unchanged Thursday at $9.48, and rose 5% in after-hours trading. T-Mobile shares closed down about 1% at $99.50, and fell a further 1% in after-hours trading.

The deal was valued above $26 billion when the carriers originally struck it in April 2018.

Both the U.S. Justice Department and Federal Communications Commission approved the combination last year after they secured concessions from T-Mobile and Sprint, the third- and fourth-largest U.S. wireless carriers by subscribers, respectively. Those concessions include an agreement that Sprint would sell airwaves and about nine million customer accounts to Dish Network Corp. to set up a fourth nationwide cellphone carrier.

The new agreement allows either company to walk away from the merger without penalty if the transaction hasn’t closed by July 1.

T-Mobile executives have said the transition will be smooth, touting their experience handling a past combination with wireless provider MetroPCS.

The new T-Mobile will have more than 90 million U.S. customers and aims to nab more subscribers from AT&T Inc. and Verizon Communications Inc. The three companies will dominate the U.S. wireless market, though they must also compete with more newcomers, including cable companies that resell service from large carriers.

T-Mobile and Sprint have spent more than seven years pursuing a combination in some form. The two companies abandoned previous attempts in 2013 and 2017 before their boards struck an agreement in early 2018 that would allow T-Mobile to take over its smaller rival, creating a company closer in size to Verizon and AT&T.

Write to Cara Lombardo at cara.lombardo@wsj.com, Dana Cimilluca at dana.cimilluca@wsj.com and Drew FitzGerald at andrew.fitzgerald@wsj.com

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