SoftBank Group Corp. won its bid to buy a major stake in Uber Technologies Inc. at a steep discount to the company’s previous valuation in a deal that gives the world’s biggest tech investor sway over the most valuable U.S. startup.

Uber investors and employees tendered shares equal to about 20% of the company in an offer by a SoftBank-led consortium that values Uber at $48 billion—a roughly 30% discount to its most recent valuation of about $68 billion, people familiar with the matter said.

The group will end up acquiring slightly less: SoftBank itself will own about 15% of Uber, and other members of SoftBank’s bidding group will get a stake of around 3%, one of the people said.​ ​

The tender offer—an open call to buy shares in the privately held company—expired Thursday at noon Pacific time, meaning investors could have changed their minds, potentially affecting the final tally of shares available.

Uber confirmed the deal Thursday and said “we expect to support our technology investments, fuel our growth, and strengthen our corporate governance.”

A SoftBank spokesman said the company expected to close the deal in January, adding that “we have tremendous confidence in Uber’s leadership and employees and are excited to support Uber.”

As part of the deal, SoftBank also plans to invest about $1.25 billion in Uber at the most recent valuation of about $68 billion, a concession to existing Uber shareholders concerned that the purchase of lower-priced shares in the tender offer might undermine the value of their remaining stakes. Including that and the shares it is buying in the tender offer, SoftBank said it will pay $7.7 billion for its 15% stake.

A successful deal is critical to Uber because a series of hard-fought corporate changes are tied to its completion. The ride-hailing firm will add six directors—including two from SoftBank—and expand voting rights for all investors. For SoftBank, the deal is a high-stakes bet on the future of transportation, as the Japanese investor owns big stakes in several of Uber’s competitors around the globe.

A final deal would conclude months of sometimes-rocky negotiations. Uber would give significant influence to SoftBank while making it a powerful ally. A deal could bolster efforts by new Chief Executive Dara Khosrowshahi to stabilize Uber and upgrade its corporate governance after a period of scandals and conflict under his predecessor, Uber co-founder Travis Kalanick.

Uber still is reeling from allegations of sexism earlier this year by a former software engineer, which lead to a company investigation and the dismissal of more than 20 people, and claims by a former Uber security official that it engaged in corporate espionage. Uber is preparing for trial in a lawsuit from Alphabet Inc. claiming Uber stole trade secrets, and it is battling regulators over its right to operate in London, one of its biggest global markets. It also recently disclosed a massive hack of the company more than a year ago that Uber said executives tried to conceal.

Uber gains a powerful backer in SoftBank CEO Masayoshi Son. His firm has a stake in all of the largest global ride-hailing firms, including Didi Chuxing Technology Co. in China as well as ANI Technologies Pvt.’s Ola in India and GrabTaxi Holdings Pte. in Southeast Asia.

SoftBank also holds stakes in some of the most well-known tech startups like WeWork Cos., Slack Technologies Inc. and Flipkart Group. The Vision Fund is the world’s largest technology fund.

The $1.25 billion investment would help solidify Uber’s balance sheet ahead of a possible initial public offering in 2019. Although the company isn’t pressed for cash—it had nearly $5 billion at the end of this year’s third quarter—it has been working to curtail costs after posting $2.52 billion in combined losses over the past two quarters, despite rising revenue and ride bookings.

SoftBank is set to appoint to Uber’s board Rajeev Misra, who helms the $93 billion Vision Fund that SoftBank is tapping for the deal, the people familiar with the matter said.

It also is likely to appoint Marcelo Claure, the CEO of Sprint Corp.,​though SoftBank Vice Chairman Ron Fisher also has been under consideration, the people said.

All three men are directors at SoftBank, meaning whichever two are chosen, the Uber and SoftBank boards would share three directors in common, as Yasir Al Rumayyan, the managing director of Saudi Arabia’s Public Investment Fund, already is on both boards.

SoftBank’s consortium in the investment includes Dragoneer Investment Group and Tencent Holdings Ltd.

With SoftBank simultaneously buying shares at two different prices, the deal has raised the question of Uber’s true value.

Startups and their investors typically mark a company’s valuation at the last price paid in a direct funding round. In so-called secondary-share sales, discounts are customary because the stock can’t be resold easily and the shares usually have fewer protections for owners than those purchased directly from the company. Direct and secondary investments from a single investor don’t usually occur simultaneously, especially on the scale of the SoftBank-Uber deal.

Some employees and investors have been waiting years for the opportunity to sell their stakes in Uber and may not get another opportunity before the possible IPO in 2019. Early investors could reap billions of dollars in the tender offer, including Benchmark, which made an initial $27 million investment in the company and holds a stake worth over $8 billion at Uber’s nearly $68 billion valuation.

A deal would make SoftBank one of Uber’s largest single shareholders. Venture-capital firm Benchmark, which holds a roughly 13% stake, as well as another early investor, Menlo Ventures, had said they would sell some of their shares in the tender offer. Uber co-founder and director Garrett Camp also is among those selling shares to SoftBank, one of the people said. Mr. Kalanick, the former CEO, who holds about 10% of Uber, has indicated he wouldn’t sell shares into the offer, people familiar with the matter have said previously.

It couldn’t be learned Thursday whether Mr. Kalanick retained his full stake.

The deal’s prospects have at times appeared uncertain. Benchmark and Mr. Kalanick engaged in a last-minute battle that threatened to derail it. Ultimately, Benchmark agreed, people familiar with the matter said, to put a stay on its lawsuit against Mr. Kalanick that sought the return to board control of three seats he oversees. And the former CEO allowed for a majority board vote for any future appointments he makes to the three board seats he controls, the people said.

If SoftBank had failed to reach a threshold of around 14% of shares after the 20-business-day period ended Thursday, it could have walked away. That could have thrown Uber into chaos, derailing the planned governance changes and raising the prospect of continued legal wrangling between Benchmark and Mr. Kalanick.

—Mayumi Negishi contributed to this article

Write to Greg Bensinger at greg.bensinger@wsj.com and Liz Hoffman at liz.hoffman@wsj.com