"This man will be missed," Gilbert tweeted. "Goodbye Richard working with you was such a joy but nearly as joyful as being your friend."
Bull played shopkeeper Nels Oleson on the family drama series from 1974 to 1983.
People.com confirmed he died Monday in Calabasas, Calif., but the magazine did not report what the cause of his death was.
Bull's other small-screen credits include "Voyage to the Bottom of the Sea" and "Highway to Heaven," which starred his "Little House" cast-mates Michael Landon and Victor French.