There were times when famed television personality Dick Cavett would be sitting in his Montauk home watching one of his old talk shows. He’d see a celebrity he was interviewing, point to a piece of furniture in the room and say, “That person was once sitting right in that chair.”

“And some of those were pretty extraordinary people,” says his wife, Martha Rogers-Cavett, referring to people like Muhammad Ali, Woody Allen and other prominent guests who visited Cavett’s Montauk estate.

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Cavett is now selling the house, which is situated on 19 acres of oceanfront property, for $62 million.

“It’s such a wonderful place,” Rogers-Cavett says. “He’s been here for 50 years and he uses the word ‘storybook.’ It’s just a storybook place.”

The seven-bedroom, five-bathroom home, known as Tick Hall, is one of seven Montauk Association houses designed by Stanford White in the 1880s that are referred to as the “Seven Sisters.” The nearly 6,000-square-foot home includes a wraparound porch that offers water views.

“The most important feature is the way the house is positioned so that every room has a spectacular view,” says Karen Kelley of The Corcoran Group, who is the listing agent for the house along with Tim Davis. “You can see for miles. You really feel like you’re all alone at the top of the world.”

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The property, which is next to roughly 170 acres of conservatory parkland, includes a swimming pool, freshwater pond, tree-covered walking trails, a Japanese pergola and a pathway that leads to a cove and private beach that locals refer to as “Cavett’s Cove.” The home features a living room with a fireplace, formal dining room, white country kitchen that opens to a porch, a library with a fireplace and a master suite that boasts a sleeping porch. Atop the house is a bell tower.

Cavett, 80, bought the house in 1965 after renting it for the summer. The original home, built in the 1882, burned down in 1997, leaving only the chimney. Cavett and his then-wife, actress Carrie Nye, who died in 2006, had an exact replica built between 1999 and 2001. The house was the subject of the 2003 documentary, “From the Ashes: The Life and Times of Tick Hall.”

In 2008, Cavett sold 76.8 acres of his estate, including 1,000 feet of oceanfront, to state and local government entities for $18 million.

Cavett was host of “The Dick Cavett Show,” which aired on various networks starting in the late 1960s. A conversational talk show host, Cavett interviewed a wide range of prominent celebrities, including Ali, Allen, Judy Garland, Groucho Marx, Jimi Hendrix, Marlon Brando, John Lennon, Lucille Ball, Jackie Robinson and many others.

Kelley says that Cavett, enjoying something of a renaissance in his career, has been featured in plays and has been traveling for speaking engagements. With multiple residences, including one in Manhattan, the Cavetts have not used the Montauk estate much in the past few years and decided it was time to sell.

“We’re just so busy that we can’t get out as much,” Rogers-Cavett says. “He said, ‘This is the right time, before something happens and we don’t have a choice. It’s better to move on and let someone else have a turn.’ ”