New prime minister or not, Larry the cat is here to stay.

Moments after Prime Minister Boris Johnson pulled out of Downing Street for the last time on Tuesday, a familiar brown-and-white tabby cat slipped out of the lacquered black door of No. 10 and perched serenely on the doorstep.

Larry the Cat was staking his claim to Downing Street, as a new prime minister — his fourth — prepared to move in to one of the world’s most famous addresses.

A feline symbol of continuity, Larry will greet the house’s next occupant, Liz Truss, when she arrives on Tuesday afternoon, as he did Mr. Johnson and his predecessor, Theresa May, when they took up residency.

The cat was taken in by Downing Street’s staff in 2012 as a rescue stray to be a pet for the children of Prime Minister David Cameron. In subsequent years, he was given the exalted title of chief mouser to the Cabinet Office, a post he has carried out with mixed results, depending on who is passing judgment.

In his farewell remarks, Mr. Johnson gave Larry a shout out, noting that he had overcome an initially fractious relationship with the Johnson’s family dog, Dilyn, the latest of several scratchy relations he has had with cats and dogs in the Downing Street complex. Larry,he said, was a figure worth emulating.

“If Dilyn and Larry can put behind them their occasional differences,” Mr. Johnson declared, “then so can the Conservative Party.”

For the last few years, Larry’s comings and goings have been a media staple for cameras waiting for news outside Downing Street. He has become a social media presence, with his own Twitter account that posts occasionally snarky observations about rotating cast of prime ministers who occupy the house.

Larry is part of a long tradition of cats in the British government. For centuries, the feline helpers have tackled rodent problems in the halls of power, although it was not until the late 1920s that records of payments for their upkeep started, when the Home Office made a request for a penny a day for cat food.

In 2019, during President Donald J. Trump’s visit to Britain, Larry made an appearance in photos, then held up proceedings by taking a nap under the presidential vehicle — a $1.5 million armored Cadillac known as the Beast. A year later, as Britain awaited updates on a post-Brexit trade deal, he stole the show by embarking on an ambitious (and failed) attack on a distracted pigeon.

Much like other occupants of No. 10, Larry has not escaped criticism of his job performance. British tabloids called him “Lazy Larry,” when Downing Street officials had to call in pest control to supplement his efforts. He also developed an antagonistic relationship with the Foreign Office’s own mouser, Palmerston, who has since retired from public duty.

Larry even figured in the Conservative Party leadership race. During a campaign event in August, Ms. Truss, Britain’s foreign secretary, noted that she had an “extremely positive” relationship with Larry, saying: “He frequently sidles up to me. I think I’m one of his preferred cabinet ministers.”

Perhaps sensing Larry’s popularity,Ms. Truss has suggested that the cat’s place in Downing Street will be secure. While campaigning over the summer, she told a child that “Larry is a beautiful cat,” when he suggested that the cat, not Ms. Truss, succeed Mr. Johnson as prime minister.