Össur was founded in Iceland in 1971 by Össur Kristinsson, a prosthetist. His family owned the company until 1999, when it went public and was listed on the Iceland Stock Exchange. Initially, the company served only the domestic Icelandic market, and then began to export in 1986 and expanded rapidly through a series of strategic acquisitions.
Össur has been listed on the NASDAQ Copenhagen Stock Exchange since 2009, and celebrated 20 years as a publicly traded company in 2019 by ringing the closing bell at the Nasdaq MarketSite in New York's Times Square. The company operates in three markets: bracing & support, compression therapy, and prosthetics including bionics technology.