Wilder is perhaps best known for his portrayal of Willy Wonka in the 1971 film Willy Wonka & the Chocolate Factory.
"It is almost unbearable for us to contemplate our life without him," Wilder's nephew, Jordan Walker-Pearlman, said in a statement.
Wilder, a Milwaukee native who was born Jerry Silberman in 1933, was nominated for an Oscar twice in his career — once for best supporting actor for his role in The Producers and once for co-writing Young Frankenstein with Mel Brooks.
Wilder's nephew confirmed that the actor died at his Stamford, Connecticut, home as a result of complications from Alzheimer's disease. Wilder was previously diagnosed with non-Hodgkin's lymphoma.
Walker-Pearlman said the Wilder did not disclose his illness because he did not want to disappoint or confuse his fans.
"He simply couldn't bear the idea of one less smile in the world," Walker-Pearlman said.
He co-founded the cancer outreach network Gilda’s Club — named after his wife, actress and comedian Gilda Radner, who died of cancer in 1989.
In a 2013 interview, Wilder said he still receives letters daily from children asking for an autograph.
"It's all because of Willy Wonka," he told Robert Osborne in 2013. "Sometimes it's someone who is 12 years old, sometimes it's 21 years old, sometimes it's 34 years old. But they want to have it signed."
Most recently, Wilder penned a memoir titled Kiss Me Like a Stranger: My Search for Love and Art.
His nephew said that despite Wilder's illness, he "continued to enjoy art, music, and kissing with his leading lady of the last twenty-five years, Karen."