Johnson died at his Washington state home of natural causes, according to his agent, Michael Eisenstadt.
"I worked with him for over 20 years. He was a gentleman, a great guy and a family man, an iconic figure," Eisenstadt said. "In the history of television Gilligan's Island was one of the most re-run shows. He'll be missed. He was old-time Hollywood."
The Pennsylvania-born Johnson had been the last surviving male cast member from the popular 1960s sitcom. Series star Bob Denver died in 2005. Dawn Wells and Tina Louise, who portrayed Mary Ann and Ginger, are still living.
Wells posted a photograph on Facebook of herself along with Johnson and Denver.
"My 2 favorite people are now gone. The Professor past away this morning. My heart is broken," she wrote.
A wartime pilot who earned several medals for his service, Johnson turned to acting and Hollywood after the Second World War.
He became a busy character actor, who appeared in a host of western, sci-fi and military-themed movies and TV shows, including It Came from Outer Space, The Californians, The Silent Service, Black Saddle and The Twilight Zone.
However, he was always best known for Gilligan's Island and was later a popular guest for appearances at various schools, conferences and presentations thanks to his role as high school science teacher Roy Hinkley.
Nicknamed the Professor, Johnson's character could famously transform coconuts and other island scraps into a radio or a generator, but apparently could not fix the castaways' leaky boat.
Though Gilligan's Island ran only three seasons on CBS in the late 1960s, it found a myriad of fans through reruns and in subsequent reunion films.
Johnson continued to act after Gilligan's Island — with appearances on shows such as Lassie, Newhart, Dynasty and Roseanne — and always remained proud of its pop culture influence and his most famous role.
"It amazes me. I have received mail throughout the years from young viewers from all over the world, year after year, who were so influenced by the Professor's smarts that they became science buffs and are now real professors, doctors and scientists. It makes me proud," he wrote on his website.
Johnson published a memoir, Here on Gilligan's Isle: The Professor's Behind-The-Scenes Guide to Everything You Ever Wanted to Know About Gilligan's Island, in 1993.
Married three times, Johnson is survived by his wife, actress Constance Dane, as well as his daughter, Kim, and stepson, Courtney. His son, David, died of AIDS at age 39 in 1994 and Johnson became active in AIDS fund-raising efforts.