He will also play a role in evaluating the “living wills” that large banks must submit to demonstrate that, in the event of failure, their businesses could be wound down without requiring government assistance. Here, too, the banks have grappled with regulators over the stringency of the requirements.

And he must wrestle with which banks deserve tougher Fed scrutiny. The 2010 Dodd-Frank law requires banks with assets of more than $50 billion to face a stricter set of rules. While there is a consensus that the government should ease the regulatory burden on community banks and limit the most stringent regulations to the very largest financial institutions, writing new rules remains a challenge. Some within the industry, including big bank trade groups, want the Fed to use a “risk-based” assessment, versus a size threshold, to determine which banks warrant tougher scrutiny. Other banks, particularly smaller regional firms, say the threshold should be raised to $250 billion from $50 billion. The Fed has already eased the qualitative provision of the stress tests on banks with less than $250 billion in assets.

Mr. Quarles is less likely to have an immediate influence on monetary policy, but he has criticized the Fed for trying too hard to stimulate the economy, and he is expected to favor raising interest rates more quickly.

He said at his confirmation hearing that the Fed should adopt a mathematical formula for determining the proper level of its benchmark rate. Some conservatives say that such a rule would make Fed policy more stable and predictable, which in turn would benefit the economy. But the idea is strongly opposed by the rest of the Fed’s board, which argues that rules are helpful as references, but that policy making ultimately requires discretion.

Mr. Quarles, 60, is a lawyer by training who worked in the financial industry before joining the Treasury Department in 2002 as assistant secretary for international affairs under President George W. Bush. He later served as under secretary for domestic finance. After leaving public service in 2006, he became a partner at the Carlyle Group and then helped to found the Cynosure Group, a private equity firm based in Utah.

He is related by marriage to Marriner S. Eccles, the Fed’s chairman from 1934 to 1948 and the namesake of the building where Mr. Quarles will now have an office.