"Richard's much-loved family announce with sadness that their dear father, grandfather and great-grandfather passed away peacefully at 10 pm on Christmas Eve," the statement said.
The tear-jerking tale is about a group of rabbits searching for a new home after the destruction of their warren, encountering perils along the way.
The book, his first novel, was published in 1972, made into an animated film in 1978 and was later into a television series which ran from 1999 to 2001.
The book is taught in British schools and he even created "Lapine", a fictional language, for it.
Adams also wrote Shardik and The Plague Dogs.