Mr. Williams would also bring a seasoned policymaking hand to a Fed that is short on them. Jerome H. Powell, the Fed’s newly appointed chairman, has been at the Fed since 2012, but he is a lawyer by training and not — unlike Ms. Yellen and most of her recent predecessors — an economist. The Fed’s vice chairmanship is vacant, and the candidate President Trump has been reported to favor, Richard Clarida, a Columbia University economist, has little policy experience. Three other positions on the seven-member board of governors are also vacant, and several regional bank presidents are new in their roles.

The relative inexperience at the top of the Fed made finding someone with practical experience a priority, two people close to the search process said. The search committee, these people said, wanted a candidate who understood the Fed’s inner workings and who would protect the Fed’s independence.

But Andrew Levin, a Dartmouth economist and former Fed staff member, said there are also risks to picking an insider. Fed officials failed to appreciate the risks posed by the housing bubble in the mid-2000s, for example, even as some outside voices tried to raise the alarm.

“The problem with picking a longtime Fed insider is it just amplifies the risk of groupthink,” Mr. Levin said, “and I think groupthink has been proven to be a very serious threat at the Fed.”

Mr. Williams also has less experience with financial markets than many past New York Fed chiefs. The bank’s president and its staff are traditionally responsible for communicating Fed decisions to Wall Street, and for interpreting financial markets’ reactions for Fed policymakers.

Mr. Williams was chosen by a search committee headed by two members of the bank’s board: Sara Horowitz, founder of the Freelancers Union, a New York-based labor organization, and Glenn Hutchins, a private-equity investor and philanthropist. Under the Dodd-Frank financial reform law enacted after the financial crisis, board members who represent financial institutions regulated by the Fed are excluded from the appointment process.

Mr. Williams’s appointment was also approved by the Fed’s board of governors.

In a statement announcing the decision, Mr. Hutchins praised Mr. Williams as someone who has a rare mix of policy expertise and management experience and who “understands the plumbing of the financial system.” In a call with reporters, Mr. Hutchins and Ms. Horowitz also cited Mr. Williams’s record of community engagement in San Francisco and his progress in diversifying the bank’s senior leadership.