The company's name is derived from the Swiss unofficial national flower, the Edelweiss, which is also painted on its aircraft.

[5] Until November 2008, Edelweiss Air was wholly owned by Kuoni Travel and had 190 employees,[6] when the operating rights were sold to Swiss International Air Lines, in exchange for sale rights of hotel capacities via the Swiss sales network.

[8] In July 2015, it was announced that Edelweiss would receive four Airbus A340-300s between 2017 and 2018 previously operated by its parent Swiss International Air Lines.

[9] In November 2015, Edelweiss introduced a revised livery on one of its Airbus A320-200s which was subsequently applied to the rest of the airline's fleet.

[12] On 6 January 2025, Edelweiss Air through a media release announced that the airline will discontinue flights to Havana, Cuba due to declining demand of passengers and the unexpected current conditions at Jose Marti International Airport.