Craven wrote and directed A Nightmare on Elm Street in 1984. His Scream franchise was reported to have grossed more than $100m (£65m) in the US.
He wrote, directed and edited his first film, The Last House on the Left, in 1972.
A tweet from his Twitter account featured a picture of him with the dates 1939-2015.
Craven was credited with reinventing the teen horror genre when the first film featuring Freddy Krueger was released in 1984 starring a then-unknown Johnny Depp.
He had more recently signed deals to develop television programmes, including the new Scream series for MTV. He had also been working on a graphic horror novel series.
Reflecting on his career, he once said in an interview: "I tried to make movies where I can honestly say I haven`t seen that before and to follow my deepest intuitions and in some cases literally my dreams."
Actors posted tributes on social media including actress Courtney Cox, who starred in Craven`s 1996 Scream and appeared in the franchise`s three subsequent films.
She said: "Today the world lost a great man, my friend and mentor, Wes Craven. My heart goes out to his family. x"
Rose McGowan, who also featured in the original Scream, said: "Thank you for being the kindest man, the gentlest man, and one of the smartest men I`ve known. Please say there`s a plot twist."
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