Elvstrom, who died Wednesday at his birthplace in Hellerup, won four consecutive Olympic gold medals between 1948 and 1960.
His Olympic streak has only been matched in sailing by Briton Ben Ainslie, who clinched his fourth gold medal in a row in 2012.
Elvstrom retired from Olympic sailing after competing at Seoul as a 60-year-old in 1988, his eighth Games over a 40-year career.
Named Denmark's sportsman of the century in 1996, he also won 11 world championships and seven European championships.
"Saddened to hear the legendary Paul Elvstrom has passed away. He was an inspiration to pretty much anyone who stepped foot on a sailing boat," Ainslie wrote on Twitter.
Elvstrom's gold medals all came in single-handed dinghies -- the Firefly at London in 1948 and the Finn (Ainslie's class for three of his golds) in Helsinki in 1952, Melbourne in 1956 and Rome in 1960.
Elvstrom also competed in the two-man Star in 1968 and the three-person Soling in 1972, and raced with his daughter Trine in the two-handed Tornado catamaran in 1984 and 1988.
"He was a great hero for Denmark and for the world of sailing. He inspired a lot of people," fellow Dane Anne-Marie Rindom, a Rio 2016 Olympic bronze medalist, told World Sailing.
Off the water, Elvstrom pioneered new sailing equipment and was an early advocate of sailing-specific fitness training.
Recognizing the need to sit or "hike" out from his boat for prolonged periods of time, Elvstrom advanced the use of footstraps and trained with straps attached to a bench in his garage.
His self-bailing bailer was an innovation, while he also contributed to a number of books on racing rules and tactics.
In 2007, Elvstrom was one of the first six inductees into the World Sailing Hall of Fame.
He is reported to have once said: "You haven't won the race if in winning the race you have lost the respect of your competitors."