Industry groups such as the Mortgage Bankers Association and key congressional Democrats welcomed the nomination, citing her regulatory background. Ms. Thompson has been serving as the FHFA’s acting director since June.

Fannie and Freddie are central players in the market for home loans, buying mortgages from lenders and packaging them for issuance as securities that are guaranteed by the firms. The arrangement allows lenders to offer the popular 30-year fixed-rate mortgage.

The two mortgage-finance giants have been under government control since the 2008 financial crisis. In the run-up to the crisis, they took on increasing risks, primarily to compete with Wall Street firms and later because lawmakers wanted them to support a weakening housing market.

The Biden administration has said it isn’t in any rush to return Fannie and Freddie to private hands, a reversal from the Trump administration, which pushed to put the companies on a path to exit conservatorship. Progress was slow and the Trump administration ultimately ran out of time.

The administration is instead expected to use Fannie and Freddie to support its general affordable-housing goals and a push to close a racial homeownership gap. The white homeownership rate is at roughly 72%, while the rate is 42% and 48% for Black and Latino borrowers, respectively, according to the Urban Institute. Just 3% of the loans Fannie purchased in 2020 were for Black borrowers, the company said earlier this year.

Ms. Thompson has signaled that she believed Fannie and Freddie could better address the racial homeownership gap.

“There is a widespread lack of affordable housing and access to credit, especially in communities of color,” she said earlier this year.

Ms. Thompson isn’t the administration’s first pick for the top FHFA role. The White House had identified another candidate to become FHFA director but held off on its plans amid pushback from congressional Democrats, including members of the Congressional Black Caucus who supported Ms. Thompson.

“It is in part due to the past and ongoing lack of representation of people of color in the senior ranks of our financial services regulators that we see stark racial and economic inequities throughout our country today,” House Financial Services Committee Chairwoman

Maxine Waters

(D., Calif.) said in a September statement endorsing Ms. Thompson.

Leadership atop the FHFA is important because it is one the most powerful jobs in the $11 trillion mortgage market, helping to determine who gets access to mortgage credit and on what terms.

Ms. Thompson has served as FHFA acting director since the summer. The White House dismissed Mr. Calabria after the Supreme Court ruled the president was free to remove the agency’s director at will.

She has spent more than four decades in government and has worked at the FHFA since 2013, overseeing regulatory policy and other matters related to Fannie, Freddie and the Federal Home Loan Banks, a network of government-chartered cooperatives that provide cheap funding to commercial lenders and other financial firms. She also worked at the Federal Deposit Insurance Corp. for more than 23 years.

Write to Andrew Ackerman at andrew.ackerman@wsj.com