Former Chancellor Rishi Sunak, who warned that Liz Truss’ economic plans for Britain were a “fairy tale,” won the contest to succeed her as prime minister on Monday, taking over the world’s sixth-biggest economy at a time of deep financial and political turbulence.

Mr. Sunak will formally enter Downing Street after his only remaining rival for the job, former defense minister Penny Mordaunt, said on Twitter she would drop out of the contest. “Rishi has my full support,” she wrote.

Mr. Sunak’s rise to the top job in Britain marks a historic moment. The grandson of Indian immigrants to Britain, the 42-year-old will be the U.K.’s first person of color and the first Hindu to lead the country. But his success will be determined by how well he manages the growing challenges to Britain’s economy as high inflation and a looming recession create a sense of growing despair.

The former hedge-fund manager arrives with a mandate to bring calm to the ruling Conservative Party following a period of unparalleled chaos that will see the country run by three prime ministers in seven weeks—a first for the U.K. On Sunday night, his main rival for the job, the colorful but controversial former leader Boris Johnson, pulled out of the leadership race, citing the fact that he couldn’t unite the party.

Mr. Sunak takes over from Ms. Truss, who became the shortest-serving prime minister in British history after her flagship economic program to stimulate the economy with tax cuts during rising inflation was rejected by investors, causing the pound to sink to a record low and the Bank of England to intervene in bond markets to stabilize the price of U.K. government debt.

On Monday, financial markets reacted positively to Mr. Sunak’s victory. Yields on government debt fell as investors bet that Mr. Sunak, an experienced treasury official, will oversee cuts to public spending to shore up the nation’s finances.

The decision caps Mr. Sunak’s second attempt to secure his place as prime minister in months. He campaigned over the summer to become British leader but lost to Ms. Truss. During the campaign Mr. Sunak criticized Ms. Truss’s plan to borrow funds to immediately cut taxes. He said Britain’s high inflation, which is currently at 10.1%, needed to be tackled first before any taxes were cut.

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The broader outlook, however, is grim. Mr. Sunak will likely face a winter of discontent as inflation, fueled by rising energy costs from the war in Ukraine, increases faster than wages, and a recession takes hold that economists think could last a year. The early stages of his tenure are likely to be punctuated by worker strikes and questions about whether electricity blackouts will be needed as Russia restricts gas exports to Europe.

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Mr. Sunak represents an unusual mix of both continuity and newness at the top of British politics. He grew up in Southern England to parents of Indian origin, his father was a doctor and his mother ran a pharmacy. Mr. Sunak attended Winchester—an elite private school that has produced several British prime ministers—before attending the University of Oxford, then finding a job at Goldman Sachs. He married Akshata Murty, the daughter of an Indian billionaire businessman. The pair met while Mr. Sunak was studying for an M.B.A. at Stanford. He co-founded a hedge fund called Theleme Partners.

As the wealthiest member of the House of Commons, Mr. Sunak could find himself in the uncomfortable position of explaining support for spending cuts that could make life harder for the working classes. Backers say he will argue that sound finances will allow Britain’s economy to improve competitiveness to create broader prosperity down the road.

In 2015, Mr. Sunak was elected to parliament in Yorkshire, a northern English and mostly white agricultural district. Mr. Sunak took his parliamentary oath to the monarch on the Hindu scripture, The Bhagavad Gita, and had to explain to many of his farming constituents that he didn’t eat beef. But he quickly proved popular and moved to a Yorkshire manor.

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Mr. Sunak was caught up in a scandal of his own. His wife Ms. Murty this year had to change her tax arrangements after admitting she benefited from tax rules that allowed her to pay no U.K. tax on her worldwide income. She says she changed that status and now pays U.K. tax on that worldwide income. The debacle made some Tory lawmakers question whether Mr. Sunak was too wealthy to connect with the party’s blue-collar voters.

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