Saudi Prince al-Waleed bin Talal has agreed to sell half his stake in Four Seasons Hotels and Resorts to co-owner Bill Gates, giving him control in a deal that values the luxury hotel operator at $10 billion.

Under terms the companies announced Wednesday, Mr. Gates’s Cascade Investment LLC would pay $2.21 billion for a 23.75% stake in the Four Seasons held by Prince al-Waleed’s Kingdom Holding Company.

Kingdom and Cascade have held equal stakes in the company since the partners took it private in 2007. When the sale is complete, Cascade will hold 71.25% of the hotel operator, while Kingdom will keep a 23.75% stake. Four Seasons founder and Chairman Isadore Sharp retains his 5% holding.

Four Seasons Chief Executive Officer John Davison said with Cascade taking control, he expects the luxury lodging company to ramp up its commitment to new technologies and Four Seasons-branded residences. The company also will pursue more environmental, diversity and other issues that appeal to younger travelers.

“We want to preserve our heritage brand but also evolve it for the next generation of luxury consumers,” Mr. Davison said.

Kingdom Holdings has listened to offers for its stake in the Four Seasons for years, from everyone from Chinese insurance companies to European luxury groups, said Sarmad Zok, CEO of Kingdom Hotel Investments. But he said that Kingdom was holding out for the right investor and he considered the $10 billion enterprise value a “magic number.”

The partners took Four Seasons private in 2007 in about a $3.8 billion deal, then the 2008 financial crisis upended the business. Kingdom marked down the value of its Four Seasons holding every year between 2008 and 2012, according to annual reports it publishes because a portion of Kingdom trades in Riyadh.

But the company has ramped up its expansion in recent years. It now operates 121 hotels and resorts and 46 residences, with a pipeline of more than 50 projects, according to a company spokeswoman. That compares to 74 hotels and resorts and 19 branded residences in 2007.

The pandemic has hit most hotels hard, and the new Delta variant has undercut the industry’s nascent comeback. But the luxury segment has done better than most, in part because declines in corporate travelers have been partially offset by the rise in affluent leisure travelers.

Bill Gates’s investment fund will pledge $1.5 billion for climate projects if Congress enacts an infrastructure bill. The Microsoft co-founder and Energy Secretary Jennifer Granholm told the WSJ how public-private partnerships can spur innovation. Photo: Gates Ventures The Wall Street Journal Interactive Edition

The segment’s four-week moving average through August 28 produced revenue per available room of about $207, or nearly even with the same period in 2019, according to hotel data tracker STR. While occupancy rates were lower, average daily room rates stood at $343.23, up from $284.09 in 2019, STR said.

Still, like hotels across all price ranges, Four Seasons has suffered from an acute labor shortage. At one Four Seasons hotel, the general manager made coffee for guests, while at another the director of finance helped tidy up a room, Mr. Davison said.

“In some limited cases, we’ve even limited our occupancy,” he added.

Efforts to expand the company’s footprint and boost revenue sometimes caused tension between Cascade and Kingdom, according to former Four Seasons executives, former board members and business partners. Mr. Zok on Wednesday played down any infighting between the partners.

“Shareholders are like married couples. People have different sensitivities,” he said. “That’s fine as long as they collectively recognize that the best idea prevails. Our relationship was healthier than at other private companies.”

A Cascade spokesman declined to comment on the relationship.

Keeping Four Seasons growing at its current pace could represent a challenge, analysts and industry executives said. The company is now doubling up with more than one hotel in places like New York City and Boston, an unusual move for a luxury operator when most city hotel owners like exclusivity.

“There are still plenty of places out there for Four Seasons, though not as many as before,” said Dan Peek, president of the hotel group at Hodges Ward Elliott, hotel broker and investment banking firm, noting that Latin America was still largely untapped opportunity.

Mr. Davison said another growth path for the company would be stand-alone branded Four Seasons residences, an increasingly popular product offered by luxury chains.

He and Mr. Gates don’t necessarily agree on everything. Mr. Gates, the Microsoft Corp. co-founder, predicted last year that about half of business travel would go away in the pandemic’s aftermath. Mr. Davison, like most other hotel executives, sees it differently.

“I see it as a short term challenge,” he said. “We are optimistic about business travel returning.”

Write to Craig Karmin at craig.karmin@wsj.com