Carpenter wrote all 26 episodes of the 1970s show - about an "eccentric, dishevelled" time-travelling wizard - winning him international recognition and a Writers Guild award.
He later wrote the 1980s hit ITV show Robin of Sherwood, first starring Michael Praed and then Jason Connery.
Author Anthony Horowitz, who worked with Carpenter, called him a "mentor".
Speaking in the Guardian
 last year, Horowitz recalled how Carpenter gave him his first job in television.
"I had absolutely no experience, had never written for TV, and really had no inclination to be a television writer.
"But Richard took me on. I was an apprentice to him really; he was my mentor.
"Working with Kip on Robin of Sherwood was the high point of my career, in terms of the fun and sheer energy," said Horowitz.
Carpenter later established production company Gatetarn, along with producer Paul Knight and Sidney Cole, co-creating series including Dick Turpin, and its New Zealand-based follow-up The Adventurer.
With a portfolio of work which included The Adventures of Black Beauty, The Famous Five and a TV adaptation of The Borrowers, he was honoured with a Children's Bafta in 2000.
Plans for a big screen adaptation of Catweazle are understood to be under way.
Carpenter also wrote novelisations of his many TV series including The Ghosts of Motley Hall and Smuggler.
He is survived by his wife, Annabelle, two children and two grandchildren.
Richard 'Kip' Carpenter, the creator of cult children's TV series Catweazle, has died at the age of 82.