President Biden warned in his farewell address to the nation last week that an oligarchy is taking shape in America. In Washington, the oligarchs are already here, buying big houses.

Counting President-elect Donald J. Trump himself, there are at least a dozen billionaires among his cabinet picks and those headed for senior roles in the new administration. Elon Musk tops the list with a $429 billion net worth, according to Forbes, making him the world’s richest man. Mr. Trump weighs in with an estimated $6.8 billion.

It is an extraordinary concentration of wealth in a city where power has always been more important than money, but is now more than ever intertwined with it. Mr. Trump campaigned as a populist defender of the American working class, but he has put some of his richest donors in commanding roles in the top reaches of government. A number will oversee the very industries that produced their fortunes.

“It’s tempting to liken this to the Gilded Age, but John D. Rockefeller didn’t actually run McKinley’s campaign or move into the White House,” said Michael Waldman, who was President Bill Clinton’s chief speechwriter and is now president and chief executive of the Brennan Center for Justice, which promotes legal system reforms and works to curb money in politics. He was referring to Mr. Musk, who spent more than $250 million to help Mr. Trump win and is now expected to have an office in the White House complex.

One of the most immediate effects in Washington has been an explosion in the luxury real estate market.

The financier Howard Lutnick, Mr. Trump’s choice to be commerce secretary (worth $1.5 billion, according to Forbes), last month closed on the French Chateau-style home of the Fox anchor Bret Baier on Foxhall Road for $25 million, a record for the area. Scott Bessent, the nominee for Treasury secretary (his financial disclosure statement shows he is worth in excess of $700 million) has looked at a $7 million Federal-style house on N Street in Georgetown, once the home of the syndicated columnist Joseph Alsop.

The 1850 Italianate-style Georgetown home of the late Boyden Gray, an influential lawyer for Republican presidents, sold last month for $10.5 million. Real estate agents would not disclose the buyer, but they did say they were running short of trophy houses in Washington because of a second-term Trump bump.

“We’ve really been overwhelmed by the wealth factor that has come to Washington since the election,” said Jim Bell, an executive vice president of TTR Sotheby’s International Realty. He said agents have resorted to calling their Washington clients and asking if they’d be interested in selling to the newcomers.

The journalist and author Sally Quinn got one such call from an agent who told her she could get twice the price for the 18-room, 1790s Georgetown home she shared for more than 30 years with her husband, the late Benjamin C. Bradlee, the famed executive editor of The Washington Post. The house was once owned by Robert Todd Lincoln, Abraham Lincoln’s son.

Ms. Quinn said she was happy to get the call, but adamant: “I said, ‘Never.’ This is my home.”

It is unclear where Mr. Musk will live in Washington, although there are local media reports that he is trying to buy the Line Hotel in the buzzy, bar-heavy neighborhood of Adams Morgan and turn it into a private club. A spokeswoman for Mr. Musk, the Tesla founder whose rocket company, Space X, has billions of dollars in contracts with the federal government, did not respond to a request for comment.

Mr. Musk is expected to have an office in the Eisenhower Executive Building across from the White House as the co-leader of the unofficial Department of Government Efficiency. His partner in the effort is Vivek Ramaswamy, a pharmaceutical entrepreneur with a net worth of $1 billion, according to Forbes, who is also planning to run for governor of Ohio, a seat that becomes open in 2026.

Jonathan Taylor, a founder and managing partner of TTR Sotheby’s, said that the rich with connections to the administration, although not necessarily a part of it, are moving here too. “There are a lot of very wealthy people looking for a seat at the table,” he said.

That is hardly surprising, said David Rubenstein, the billionaire co-founder of the private equity Carlyle Group.

Big donors, he said, “would like to get the policies they believe in from the federal government — more oil drilling, easier antitrust policy, more favorable crypto policy, less bank oversight. They also want more support for helping American companies invest overseas, and have ready access to government officials.”

Washington housing, he said, was also a relative bargain for them. “If you want to buy a home in New York or Southampton, a really good house, it could cost $100 million to $150 million,” he said. “You can’t spend $25 million in Washington even if you try.”

Mr. Rubenstein, who served as deputy domestic policy adviser to President Jimmy Carter, said he looked at Mr. Baier’s house when it was on the market but decided to stay in the home in Bethesda, Md., where he has lived for decades. He also owns the sprawling compound in Nantucket that President Biden has used for his family Thanksgiving vacations.

Democrats have money too, although Mr. Biden’s Cabinet is largely filled with single- and double-digit millionaires. His current White House chief of staff, Jeffrey Zeints, listed assets ranging from $68 million to $338 million on his 2024 financial disclosure form. One outlier is Penny Pritzker, an heir to the Hyatt hotel fortune who was a commerce secretary for President Barack Obama and served as Mr. Biden’s special representative for Ukraine’s economic recovery. She has a current net worth of $4.1 billion, according to Forbes.

Mr. Trump’s billionaires have substantially bigger assets than those top officials who came to Washington for his first term, which was considered the wealthiest administration in American history at the time. Mr. Trump’s first secretary of state, Rex W. Tillerson, the former chief executive of ExxonMobil, had assets of between $289 million and $350 million in 2017. He lasted a little more than a year before Mr. Trump fired him by tweet.

Some tech billionaires, who moved here in part to have access to the White House and Congress as their industry came under growing government scrutiny, have been in Washington for years.

Jeff Bezos, the Amazon founder and owner of The Washington Post, paid $23 million in 2016 for the former 27,000-foot Textile Museum on a grand street in the Kalorama neighborhood. The Silicon Valley venture capitalist Peter Thiel, who donated more than $1 million to Mr. Trump in 2016, paid $13 million in 2021 for a home on Woodland Drive owned by Wilbur Ross, the secretary of commerce in Mr. Trump’s first term. Eric Schmidt, the former chief executive of Google, paid $15 million for the home across from Ms. Quinn on N Street, where Jacqueline Kennedy lived for a short time after her husband’s assassination in 1963.

“These are really rich people,” said Kara Swisher, a journalist who chronicles the tech industry and is a former opinion writer for The New York Times. “As much as they like to have an image of not being spendy, they’re all really spendy. They all have private planes, they all have assistants, they have people who get them the kind of nuts they want.”

Washington neighborhoods in high demand, real estate agents said, were Kalorama, Massachusetts Avenue Heights off the embassy-lined street of the same name, and Georgetown, whose cobblestone lanes were traditionally the preserve of Washington’s old-line elite. Not anymore, said Jamie Peva, a real estate agent with Washington Fine Properties who has sold houses in Georgetown for 33 years.

“That whole WASP hegemony that started to decline in the ’80s just continued to decline,” he said. “All of a sudden tech starts to come in. It’s a meritocracy.”

A few of the billionaires will presumably not need homes in Washington. Charles Kushner, a real estate executive whose companies are worth $2.9 billion, according to Forbes, is to live in Paris as the U.S. ambassador to France. Mr. Trump pardoned Mr. Kushner, a major donor to Mr. Trump’s 2024 campaign, in the last days of his first term. In 2004, Mr. Kushner pleaded guilty to tax evasion, retaliating against a federal witness and lying to the Federal Election Commission.

Warren Stephens, an investment banker worth $3.3 billion, according to Forbes, is to live in London as the U.S. ambassador to Britain. In 2016, Mr. Stephens gave $2 million to a group aiming to stop Mr. Trump from winning the Republican presidential nomination and in the 2024 primaries backed Republican candidates other than Mr. Trump. In April, after it became clear that Mr. Trump would be the Republican nominee, Mr. Stephens donated more than $3 million to his campaign.

Tilman Fertitta, the owner of the Houston Rockets and a longtime Republican donor who is worth $10.2 billion, according to Forbes, is set to live in Rome as the U.S. ambassador to Italy.

Eric Lipton contributed reporting.