Zevon, known for songs including "Werewolves of London" and "Excitable Boy," died Sunday at 56.
"He was a poet and a storyteller and a good friend of ours," Letterman said. "We all knew this was coming, hoping that it wouldn't, but yesterday afternoon in California the inevitable happened. So we're very sad about that."
He noted that Zevon had appeared as a guest on the program and Letterman's old NBC "Late Night" show more than a dozen times and had filled in for bandleader Paul Shaffer nearly two dozen times.
"People are always asking me what do I like about his music," Letterman said.
"It was just thundering and exciting and rhythmic and complicated and unusual rock 'n' roll," he continued. "It was not the kind of rock 'n' roll you would hear much of. And then the lyrics, oh my God, the lyrics were so vivid. Just very evocative and each song that you listened to was like watching a motion picture."
Shaffer and the band played Zevon's songs throughout the show, which ended with Letterman speaking to the camera, saying, "Goodnight, Warren, we'll see ya."
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