His arrival in September comes as Phillips and the broader art market seek to build momentum after the pandemic compelled the industry to pivot online. Last year, Phillips’s sales fell 16%, to $760 million. Its performance in Asia proved a bright spot, with sales in its Hong Kong hub surging to $152 million last year, up 24% from a year earlier. So far this spring, online and telephone bidding competition for contemporary art appears to be perking up in live-streamed sales conducted from New York, London and Geneva—signs that the market could rebound soon as auctions can once again be conducted with bidders in the room.

“After moments of trauma, history often sees an explosion of cultural and economic activity,” Mr. Brooks said in an interview before the announcement. “We’ve got a huge opportunity for growth here.”

Mr. Brooks, an Oxford native, previously worked as chief financial officer of Schroders, the asset manager. He then spent 11 years working in several management roles at Christie’s, joining as chief financial officer in 2009 during the worst of a recession that compelled him to winnow budgets and staff. He was deputy chief executive when he left Christie’s last August.

At Phillips, he will assume a role held for the past seven years by Edward Dolman, another former Christie’s executive. Mr. Dolman is often credited with engineering a turnaround at Phillips. When the house’s Russian owners, Mercury Group, hired Mr. Dolman to become Phillips’s president and chief executive in 2014, the house’s edgy, emerging art offerings were largely ignored by the industry’s duopoly, Sotheby’s and Christie’s, dealers said. Mr. Dolman set about hiring dozens of high-profile specialists—including Arnold Lehman, former director of the Brooklyn Museum—and over time, the house gained a reputation for offering new and modern masters for attention-grabbing prices. Last December, the house held an auction that included a David Hockney artwork, “Nichols Canyon,” which sold for $41 million.

Sales were $399 million in 2014, the year Mr. Dolman joined Phillips, and in 2020 they had nearly doubled. Under his tenure, the house said it also roughly doubled its head count, to 445 people, and nearly tripled its ranks of active clientele, to over 11,000 people. Five years ago, it opened a salesroom in Hong Kong and recently teamed up with a Beijing auctioneer, Poly Auction, to conduct joint sales, with Phillips’s mandate to source and funnel more emerging art from the West to mainland Chinese collectors. Highlights for its biggest sale of the season in New York in late June will make preview stops in several Chinese cities including Shenzhen, as well as cities in Taiwan.

Mr. Dolman will shift to a newly created position of executive chairman, overseeing Phillips’s namesake holding company. He said he plans to focus more on winning top consignments and developing closer ties to collectors in Asia. He will continue to work closely with Cheyenne Westphal, Phillips’ global chairwoman, who will remain in her current role.

Mr. Brooks will take over the company’s financials and manage day-to-day operations at the auction house, which maintains four salesrooms around the world—including a New York hub on Park Avenue that is set to reopen June 15 with a larger subterranean salesroom. The job will also require Mr. Brooks to manage a far-flung staff which last year helped auction off nearly 7,000 objects in 69 sales, including 29 auctions held entirely online. That compares with sales of around 4,000 objects across 38 sales in 2014, the year Mr. Dolman took over.

Mr. Brooks is best known in art circles for helping steer Christie’s through the 2009 recession and its subsequent restructuring. He also helped that house close the deal on complex consignments like the $835 million estate of David and Peggy Rockefeller in 2018. Now, Mr. Brooks said he is eager to step into a more public-facing role as chief executive and work again with Mr. Dolman. “We get along like a house on fire,” he said.

“I want to grow a business and not always be the guy who has to deliver the bad news,” said Mr. Brooks, who collects contemporary artists and swirling ceramic pieces by British potter Mitch Pilkington.

Write to Kelly Crow at kelly.crow@wsj.com