President Biden has chosen Saule Omarova, a Cornell Law School professor, to lead the Office of the Comptroller of the Currency, the regulator overseeing the largest U.S. banks, the White House announced on Thursday.

If confirmed, Ms. Omarova, who grew up in what is now Kazakhstan, will be the first woman and the first nonwhite person to serve as comptroller of the currency. The agency, which has about 3,500 employees, is charged with setting policy around the businesses that banks engage in — from traditional ones like mergers and lending to newer efforts like cryptocurrency.

“I am deeply honored to be nominated for this role in President Biden’s administration,” Ms. Omarova said in a statement provided to The New York Times. “If confirmed, I will work hard to make sure that our banks remain stable, strong and serve the needs of the American people.”

Ms. Omarova’s nomination caps a monthslong search for the top banking regulator’s job; the Biden administration dropped two earlier candidates because progressive and moderate Democrats couldn’t agree on them. But Ms. Omarova’s nomination will require Senate confirmation — potentially an uphill battle given the 50-50 split between Republican senators and the Democratic caucus.

Ms. Omarova, who has government experience and spent time both in academia and at a white-shoe law firm, is an unusual choice. She was a policy adviser at the Treasury Department under President George W. Bush, working for the bank lawyer Randal K. Quarles, who was then serving as a senior Treasury official. Mr. Quarles had hired her away from his former firm, Davis Polk & Wardwell.

Mr. Quarles was chosen by President Donald J. Trump to be the Federal Reserve’s vice chair for supervision, the top bank regulatory position at the central bank. If Ms. Omarova is confirmed, she will be her former boss’s counterpart at the Office of the Comptroller of the Currency.

In her academic work, Ms. Omarova has proposed bold changes to the financial system, but those proposals — most notably an idea for a public infrastructure investment authority modeled on the structure of the Federal Reserve system — would not be easy to introduce from a post atop the O.C.C.

Instead, in setting a policy agenda, Ms. Omarova is likely to draw on the basic philosophy she has laid out in her work on the relationship the government should have to banks. She has criticized the notion that taxpayers often have to clean up messes left by the private sector in times of crisis but are left out of a proportionate share of private industry’s successes in prosperous times.

Ms. Omarova has also highlighted the risks to the financial system posed by the digitization of assets and the advent of cryptocurrencies, which are less tightly controlled by governments and could lead to a buildup of risk that regulators can’t see until it is too late.

Her recent work on digital assets could come in especially handy if she is confirmed. Over the past two years, O.C.C. leaders have grappled with questions about what to do about banks’ attempts to develop digital assets, as well as the proliferation of nonbank financial firms that offer banklike services on the internet.

Ian Katz, managing director of Capital Alpha Partners, a Washington research firm, said Ms. Omarova was likely to face a tough confirmation fight because, even though she was a previous appointee of Mr. Bush, some of her recent posts on Twitter could rub Republicans the wrong way.

Mr. Katz pointed to a post Ms. Omarova wrote in July: Citing a news report about a string of acquisitions of smaller companies by JPMorgan Chase, the nation’s largest bank, Ms. Omarova asked: “Does the world need JPMorgan to grow bigger and more powerful? Just wondering.”

“Everything is very partisan, and this pick will be seen as a partisan pick,” Mr. Katz said. “When you tweet, it’s easier for your opponents to pick on you.”

Senator Patrick J. Toomey of Pennsylvania, the top Republican on the Senate banking committee, which will take up Ms. Omarova’s nomination first, said in a statement emailed to journalists that he had “serious reservations about her nomination.” He characterized her writings as containing “extreme leftist ideas.”

It is not clear whether most Democrats will embrace Ms. Omarova, but she already has support from progressive members of the Senate.

Senator Elizabeth Warren of Massachusetts said Mr. Biden’s choice was “tremendous news.”

“Saule is an excellent choice to oversee and regulate the activities of our nation’s largest banks, and I have no doubt she’ll be a fearless champion for consumers,” Ms. Warren said in a statement emailed to The Times.

Senator Sherrod Brown of Ohio, the Democrat in charge of the banking committee, also expressed support. Ms. Omarova is “well versed in new financial technologies” and well equipped to “work with stakeholders across our financial system,” he said in a statement emailed to journalists.

“I call on my colleagues on the Banking and Housing Committee to support this historic nominee,” Mr. Brown added.