The Brooklyn-born DeForest, who was 85, died Monday at a hospital on Long Island, Letterman's "Late Show" announced Wednesday.
He made dozens of appearances on Letterman's shows from 1982 through 2002, handling a variety of twisted duties: dueting with Sonny Bono on "I Got You, Babe," doing a Mary Tyler Moore impression during a visit to Minneapolis and handing out hot towels to arrivals at the Port Authority Bus Terminal.
"Everyone always wondered if Calvert was an actor playing a character, but in reality he was just himself — a genuine, modest and nice man," Letterman said in a statement. "To our staff and to our viewers, he was a beloved and valued part of our show, and we will miss him."
The gnomish DeForest was the first face to greet viewers when Letterman's NBC show debuted on Feb. 1, 1982, offering a parody of the prologue to the Boris Karloff film "Frankenstein."
"It was the greatest thing that had happened in my life," he once said of his first Letterman appearance.
DeForest, given the nom de tube of Melman, became a program regular. The collaboration continued when the talk show host launched "Late Show with David Letterman" on CBS in 1993, though DeForest had to use his real name because of a dispute with NBC over "intellectual property."
Cue cards were often DeForest's television kryptonite, and his character inevitably appeared in an ill-fitting black suit behind thick black-rimmed glasses.
DeForest often drew laughs by his bizarre juxtaposition as a "Late Show" correspondent at events such as the 1994 Winter Olympics in Norway or the 25th anniversary Woodstock concert that year.
His last appearance on "Late Show," celebrating his 81st birthday, came in 2002.
DeForest also appeared in an assortment of other television shows and films, including "Nothing Lasts Forever" with Bill Murray and Dan Aykroyd.
At his request, there will be no funeral service for DeForest, who left no survivors.
By Larry McShane