Nissen died Wednesday of complications from pneumonia at UC San Diego Thornton Hospital in La Jolla, said his daughter Dagmar.
He "was a true sports pioneer," Steve Penny, president of USA Gymnastics, the sport's national governing body, said in a statement. "His vision, innovations and passion sowed the seeds for trampoline's worldwide popularity."
More than 60 years after Nissen tested his first workable prototype, trampoline debuted as a medal sport in the 2000 Sydney Olympics.
"It is something I dreamt, like people winning a million dollars," Nissen told reporters as he sat in the audience for the first night of Olympic trampoline competition.
Peter Vidmar, a 1984 Olympic gold medalist in gymnastics, called Nissen "a hero of mine."
"He was so proud that the sport he pioneered had not only become an Olympic discipline, but that its appeal was truly global," Vidmar said in a statement.
George Peter Nissen was born Feb. 3, 1914, in Blairs- town, Iowa, the youngest of four children of a Danish immigrant who ran a dry-goods store.
In high school, Nissen was a gymnast and diver when he made the serendipitous visit to the circus. Watching the acrobats rebound, he wondered if the net could help him train for his sports, he later said.
An early prototype crafted from canvas and junkyard scraps gave way to his first usable model, developed in 1934 from strips of inner-tube rubber while he was a University of Iowa student.
His coach, Larry Griswold, and the school of engineering gave him an assist.
At a YMCA summer swimming camp, Nissen tested out the bouncer. When "nobody wanted to go swimming," he knew he was onto something, Nissen told Reuters news service in 2000.
At Iowa, he was a champion gymnast and in 1937 earned a bachelor's degree in business.
With two friends, the new college graduate somersaulted his way around the country and Mexico as one of the "Three Leonardos," performing what was then called "rebound tumbling."
But Nissen wanted a catchier name and coined one after hearing the Spanish word trampolin, for "diving board" or "springboard."
He trademarked the name "trampoline" but it eventually became the generic term for the apparatus that has proliferated in so many American backyards.
In 1941, he opened Griswold-Nissen Trampoline and Tumbling Co. in Cedar Rapids, Iowa, which manufactured and sold gymnastics equipment.
During World War II, he served in the Navy while trampolines were used to train pilots to learn how to orient themselves in the air.
After the war, Nissen started heavily promoting the trampoline by staging competitions and introducing it around the world.