The author of the books about the boy wizard, J K Rowling has paid tribute to Craig's work.
"Working with Stuart Craig was one of the privileges of my life. He was a true visionary and conjured the wizarding world for the screen as nobody else could have done," she said.
"He was also one of the nicest people you ever could hope to meet. My deepest condolences to his loved ones."
Stuart worked on all eight Harry Potter films between 2001 and 2011, beginning with Philosopher's Stone and concluding with Deathly Hallows Part 2.
He later designed the Harry Potter theme parks with Warner Bros and continued his involvement in the franchise by working on the three Fantastic Beasts films released between 2016 and 2022.
Across a career spanning more than four decades, Craig won three Academy Awards and received eight further nominations.
He was awarded best art direction Oscars for Gandhi (1982), Dangerous Liaisons (1988) and The English Patient (1996.)
He was also nominated for four Harry Potter films.
His other accolades included three Baftas from 16 nominations.
David Puttnam, 83, who collaborated with Craig on The Mission (1986), Cal (1984) and Memphis Belle (1990), said: "Not only was Stuart the most inventively gifted production designer of his generation, but as a man and a departmental head he certainly ranks among the most exemplary collaborators I ever had the privilege of working with.
"Losing Stuart is a very sad day for the whole of the British film industry – he and his influence will be massively missed."
Stuart studied film design at the Royal College of Art in London before working on productions including Casino Royale (1967), Scrooge (1970) and Royal Flash (1975.)
He established his reputation with A Bridge Too Far (1977) and Superman (1978) before a breakthrough as production designer on David Lynch's The Elephant Man (1980).
Further credits included Chaplin (1992), Notting Hill (1999) and The English Patient, for which he won his third Oscar.
Craig married Patricia Stangroom in 1965, and the couple had two daughters, Becky and Laura, and four grandchildren.
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