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WASHINGTON — President Barack Obama and his wife, Michelle, who have spent the past few months slowly figuring out the rhythm of post-White House life, have taken some time to invest in local real estate: They just spent $8.1 million to buy the mansion they’ve been renting in an exclusive neighborhood here.

Last May, the Obamas decided to lease the 8,200-square-foot Tudor-style mansion in Kalorama, a Washington neighborhood that has long been home to diplomats, lobbyists, politicians and the occasional spy. The wealthy enclave is especially crowded lately: President Trump’s daughter Ivanka Trump, her husband, Jared Kushner, and Secretary of State Rex W. Tillerson have all moved into Kalorama in recent months.

The Obamas purchased the nine-bedroom home through a holding company they control, according to Washington property records posted on Wednesday. The property was previously owned by Joe Lockhart, a former press secretary to Bill Clinton who is now the top communications official for the National Football League. The sale, reported by The Chicago Sun-Times, was confirmed by Kevin Lewis, Mr. Obama’s spokesman.

“Given that President and Mrs. Obama will be in Washington for at least another two and a half years, it made sense for them to buy a home rather than continuing to rent property,” Mr. Lewis said in an email.

The couple’s younger daughter, Sasha, is still in high school. For the short term, at least, she will tether the Obamas to a heavily Democratic city where people are still reeling from the arrival of the Trump administration. The family has largely kept a low profile here, staying out of the political fray. But both Mr. and Mrs. Obama have traveled extensively in recent weeks. And without mentioning his name, the Obamas have either subtly taken aim at Trump policies or basked in their post-White House popularity.

Last week, Mr. Obama was greeted warmly by Chancellor Angela Merkel of Germany in a visit to Berlin — a stark contrast to the cool reception Mr. Trump received from European leaders hours later in Brussels. And in recent speeches, Mrs. Obama has hinted at taking on a more vocal role in politics.

“There’s just so much more we can do outside of the office,” Mrs. Obama said at an architecture conference in April, “because we won’t have the burden of political baggage.”

In May, Mrs. Obama criticized a move to change school lunch nutrition guidelines, a signature of her platform in the White House.

“You have to stop and think, ‘Why don’t you want our kids to have good food at school?’” she said at a nutrition summit meeting. “‘What is wrong with you, and why is that a partisan issue?’”

The decision to buy a home that sits two miles from the Trump White House may ultimately produce more questions than answers about where the Obamas might live in the long term: They are also keeping their home in the Kenwood neighborhood on Chicago’s South Side. But busy Kalorama is likely to stay inundated with journalists and Secret Service agents for the foreseeable future. Ms. Trump and Mr. Kushner — also an adviser to the president — have their own large Secret Service details. They rent their home for $15,000 a month, The Wall Street Journal reported in April.

The Obamas’ purchase of the Kalorama home reflects an extreme example of the upward trend in big-ticket sales around the area, according to Maxwell Rabin, a broker for TTR Sotheby’s International Realty.

“That’s a big number,” he wrote in an email about the home. “It sold in 2014 for $5.3 million.”

Residents have complained of protests against Trump, a deluge of parking problems and photographers that stake out the home of Ms. Trump and Mr. Kushner. But they tend to praise one crucial neighborhood amenity: Crawling with Secret Service agents, Kalorama is really — really — safe.

“Thinking of canceling my alarm service,” the lobbyist Tony Podesta, who lives two doors down from the Obamas, wrote in an email.