For years Mr. O’Brien has tried to book the Pulitzer Prize-winning author of “The Power Broker” and the multivolume epic “The Years of Lyndon Johnson.” And for years Mr. Caro has said no.

Mr. O’Brien, 55, started to realize his love for the biographer-historian was perhaps unrequited some eight years ago.

At the time, he had recently made the move to TBS after 17 years as a late-night host at NBC — a run that had come to an end with his brief stint behind the desk of “The Tonight Show.” Newly ensconced at “Conan” in the lower-stakes environs of basic cable, he had the freedom to give serious airtime to guests who would have gotten five-minute segments during his network days.

“We’re talking about authors, and I’m thinking, ‘Let’s get Robert Caro on — I’ll do two segments with him,’” Mr. O’Brien said. “The request went out. It was the equivalent of putting a penny in a well and never hearing the splash.”

Later invitations also resulted in polite refusals.

“The Path to Power,” the first installment of Mr. Caro’s biography of President Johnson, was published in 1982, when Mr. O’Brien was a student at Harvard. He received the book as a Christmas present from his father and soon fell under its spell, as did his roommate, Eric Reiff. They shared their new enthusiasm during a trip away from campus. ...