The Hollywood actor, known for roles in comedy classics such as Young Frankenstein and Blazing Saddles, has been hailed as one of the “great talents” of his generation.
Wilder’s nephew said he died at his home in Stamford, Connecticut, having suffered from Alzheimer’s disease, the Associated Press reported.
Jordan Walker-Pearlman said Wilder was diagnosed with the disease three years ago, but kept the condition private so as not to disappoint fans.
Mr Walker-Pearlman said: “He simply couldn’t bear the idea of one less smile in the world.”
Wilder’s friend Mel Brooks, who directed The Producers, the classic comedy in which Wilder starred, said on Twitter: “Gene Wilder-One of the truly great talents of our time. He blessed every film we did with his magic & he blessed me with his friendship.”
In 1968, Wilder received an Oscar nomination for his work in The Producers in which he played the introverted Leo Bloom.
Millions knew Wilder for his collaborations with Brooks on The Producers, Blazing Saddles and Young Frankenstein.
The last film - with Wilder playing a California-born descendant of the scientist, insisting that his name is pronounced “Frahn-ken-Shteen” - was co-written by Brooks and Wilder.
But perhaps Wilder’s most famous film was Willy Wonka & The Chocolate Factory, in which he played Roald Dahl’s enchanting candy man.
Actor Jim Carrey made reference to the 1971 hit in a tweet, writing: “Gene Wilder was one of the funniest and sweetest energies ever to take a human form. If there’s a heaven he has a Golden Ticket.”
Singer Josh Groban tweeted: “Thank you Gene Wilder for the wonderful, the weird, the pure imagination. One of my greatest heroes.”
Actor Russell Crowe said he saw Blazing Saddles seven times at the cinema with his school friends, adding: “Gene Wilder you were a genius. Rest in Peace.”
Comedian and presenter Dara O Briain tweeted: “Gene Wilder has died. Sad news, but such a life well lived. For me, Young Frankenstein just pips Wonka, but so many wonderful performances.
“Expecting to hear people were fans of Blazing Saddles, Producers and Stir Crazy, but amazing number going for See No Evil, Hear No Evil.”
Stephen Fry tweeted: “Farewell #GeneWilder, comic genius. Thank you for all those happy happy hours.”
This year has seen a long list of celebrity deaths including David Bowie, Ronnie Corbett and Victoria Wood.