The U.S. Justice Department agreed to allow Huawei Technologies Co. finance chief Meng Wanzhou to return to her home in China nearly three years after she was detained in Canada on behalf of the U.S., removing one irritant in a deteriorating relationship between the U.S. and China.

Under the agreement, entered in federal court in Brooklyn on Friday, Ms. Meng admitted remotely from Canada to some wrongdoing in exchange for prosecutors deferring and later dropping wire and bank fraud charges.

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The U.S. Justice Department agreed to allow Huawei Technologies Co. finance chief Meng Wanzhou to return to her home in China nearly three years after she was detained in Canada on behalf of the U.S., removing one irritant in a deteriorating relationship between the U.S. and China.

Under the agreement, entered in federal court in Brooklyn on Friday, Ms. Meng admitted remotely from Canada to some wrongdoing in exchange for prosecutors deferring and later dropping wire and bank fraud charges.

In a four-page statement of facts, Ms. Meng acknowledged that she made untrue statements to a bank in 2013 about the relationship between Huawei and a company it controlled that operated in Iran, leading the bank to provide services that violated U.S. sanctions on Iran.

“Meng’s admissions confirm the crux of the government’s allegations in the prosecution of this financial fraud—that Meng and her fellow Huawei employees engaged in a concerted effort to deceive global financial institutions, the U.S. government and the public about Huawei’s activities in Iran,” the acting U.S. attorney in Brooklyn, Nicole Boeckmann, said.

A representative for Huawei declined to comment.

Ms. Meng, who is 49 years old, is the daughter of Ren Zhengfei, the founder of Huawei, the world’s largest maker of telecommunications equipment and a leader in 5G technology.

The deal comes as relations between the two countries have worsened, particularly after the U.S., U.K. and Australia announced an initiative this month to provide Australia with nuclear submarines to counter China’s influence in the Indo-Pacific region.

“I hope it will open the way for the resolution of a string of other important issues that have plagued Sino-American relations,” said American lawyer Jerome A. Cohen, who has been involved in several high-profile U.S.-China legal cases.

In statements last month marking 1,000 days since Ms. Meng’s arrest, Chinese officials in Beijing and Canada said she had been arbitrarily detained and called her case “purely a political incident” aimed at obstructing China’s high-technology and scientific development. Under the deal, Ms. Meng agreed not to contradict her admissions to prosecutors.

Caught in the middle of the two superpowers is Canada, which has seen its trade with China plunge and two of its citizens detained in China within days of Ms. Meng’s 2018 arrest. According to people familiar with the matter, a deal with Ms. Meng could lead to the release of businessman Michael Spavor and Michael Kovrig, a Canadian diplomat on leave, who have been confined to separate Chinese facilities and prisons since December 2018.

Trump administration officials had discussed a similar deal with Ms. Meng’s lawyers late last year, but those efforts stalled as Ms. Meng insisted she had done nothing wrong and prosecutors required an acknowledgment that she had violated U.S. law, The Wall Street Journal has reported.

As the Biden administration has staffed its ranks at the Justice Department, officials have revisited those discussions in recent weeks, the people said. The current round of negotiations had gained more momentum in light of Ms. Meng’s desire to be reunited with her husband and children, the people said.

Some U.S. national-security experts who have urged the U.S. to take a tough line on China said they viewed the deal as a surrender that the Chinese government would use to its advantage. “I suspect that Beijing will conclude that hostage-taking works and that Washington will capitulate when pressured,” said Matt Turpin, a former China director on the National Security Council in the Trump administration.

John Kamm, executive director of Dui Hua, a San Francisco-based organization that deals with prisoner rights in China, agreed. “The Chinese will view this as giving in to a Chinese demand,” he said.

The deal to free Ms. Meng risks a backlash in Congress, where some Republicans have accused the Biden administration of being too lenient against Huawei compared with former President Donald Trump. On Thursday, Commerce Secretary Gina Raimondo told the Journal that her department would continue efforts to block Huawei from getting advanced chips.

Arrested nearly three years ago while transferring planes in Vancouver, Ms. Meng was indicted in 2018, alongside her employer, on charges of violating U.S. sanctions on Iran by misleading banks in 2013 about the Chinese company’s ties to Iran. Ms. Meng has since been confined to Vancouver, where she owns a home.

According to the statement of facts, Ms. Meng admitted that she knew Huawei controlled a company that did business in Iran, even though she told an executive at one of the banks that the company was a third party that Huawei worked with. Those statements led the bank, previously identified as HSBC, to continue its relationship with Huawei and process at least $7.5 million in transactions that violated U.S. sanctions on Iran, according to the document.

Last year, prosecutors obtained additional charges against Huawei and two of its U.S. subsidiaries, including racketeering conspiracy and conspiracy to steal trade secrets, adding pressure on the company as U.S. officials worked to persuade allies around the world to lock the telecommunications giant out of their next-generation mobile networks because of national-security concerns.

Huawei isn’t expected to be a part of the deal regarding Ms. Meng, and will continue to fight the charges it faces, the people said.

Since her arrest in December 2018, Ms. Meng has become the global face of trade and technology tensions between the U.S. and China. The Trump administration viewed Huawei as a national-security threat and portrayed Ms. Meng’s alleged coverup of ties in Iran as part of a pattern of corporate wrongdoing.

Within Huawei, Ms. Meng has become a celebrated figure, and securing her release has long been a priority for company leadership. Letters from Ms. Meng from Vancouver have been widely circulated to Huawei staff back in China, and slogans calling for her return have been emblazoned on coffee cups and other items at Huawei headquarters in Shenzhen.

The company has faced several rounds of sanctions as U.S. officials have long alleged Huawei gear could enable Chinese espionage in the countries that install it. The company has repeatedly said its gear is safe and that it would never spy on behalf of any government.

A year ago, Huawei was the world’s largest maker of smartphones after cornering about one-fifth of the global handset market. The U.S. sanctions have cut the company off from crucial computing chips and software, and its second-quarter phone shipments plunged by more than 80% from a year earlier. On Friday, a senior company executive said U.S. sanctions would cost Huawei up to $40 billion in lost smartphone revenue this year.

The renewed talks to resolve Ms. Meng’s case picked up one month after a Vancouver judge wrapped up nearly two years of court hearings tied to a Justice Department request to have Ms. Meng extradited to the U.S.

The judge had been expected to issue her decision later this year. Extraditions to the U.S. are rarely barred in Canada and the judge had ruled against Ms. Meng on a handful of key legal arguments.

The court reversals discouraged Ms. Meng, particularly during the past year, people familiar with the matter said. She has been spending most of her time in her large Vancouver home, where she is supervised by court-appointed security guards, the people said. Most days she consults with her legal team about her case, practices English with an online tutor, paints and exercises, they said. Ms. Meng hasn’t seen her husband and children since they visited her in Vancouver in the spring.

In recent weeks, developments in China related to the cases against the two Canadian men who have been detained there pointed to a possible resolution on the horizon. Last month, Mr. Spavor was sentenced by a Chinese court to 11 years on espionage charges, with the court saying he would be expelled, without specifying when. Mr. Kovrig was tried this year on similar charges but the court hasn’t announced a verdict.

Family members of Mr. Spavor have said they disagreed with the charges and Mr. Kovrig’s wife has said he was innocent. Representatives of the families couldn’t be reached on Friday.

—James T. Areddy contributed to this article.

Write to Aruna Viswanatha at Aruna.Viswanatha@wsj.com, Dan Strumpf at daniel.strumpf@wsj.com and Jacquie McNish at Jacquie.McNish@wsj.com