Gibson's son, Jon, told the Los Angeles Times he died late Monday night at his home in Malibu, Calif.
"Henry was an integral part of 'Laugh-In' for a long time, and he was brilliant," close friend and "Laugh-In" announcer Gary Owens told the Times. "He was a very funny man."
"He came in and did a poem and a full back flip. He said, 'Is that anything?' I said, 'Be here Monday,'" said George Schlatter, the executive producer and creator of "Laugh-In," recalling the day Gibson auditioned for the show.
"Henry was a sweet, gentle man. Any piece we gave to Henry took on a different shape when he read it because he infused his own whimsy and his own gentle intelligence and wit to it," Schlatter added.
Poems Gibson penned and recited on the series were compiled for two comedy albums, "The Alligator" and "The Grass Menagerie," and the book "Flower Child's Garden of Verses."
The Pennsylvania native's film credits include "The Nutty Professor," "Kiss Me, Stupid," "Nashville," "The Blues Brothers," "The 'Burbs" and "Wedding Crashers." He recently played a recurring role on the TV courtroom comedy "Boston Legal" and lent his voice to Wilbur the pig in the animated movie "Charlotte's Web."
He is survived by his sons Jon, Charles and James; his three sisters, Elizabeth Malloy, Adele Donahue and Mary Lee; and two grandchildren, the Times said.