The granddaughter of the 11th Duke of Devonshire, Andrew Cavendish, and Deborah Mitford, she rose to fame in the 1990s, walking the runway for designers including Versace and Alexander McQueen.
Tennant was among models representing the British fashion industry during the closing ceremony at the Olympic Stadium, on the final day of the London 2012 Olympics.
She married French-born photographer David Lasnet in the small parish church of Oxnam in the Scottish Borders in 1999. They had four children together.
In a statement, her family said: “It is with great sadness we announce the sudden death of Stella Tennant on 22nd December 2020.
“Stella was a wonderful woman and an inspiration to us all. She will be greatly missed.
“Her family ask for their privacy to be respected. Arrangements for a memorial service will be announced at a later date.”
A Police Scotland spokesman said: “Officers were called to an address in Duns, Scottish Borders, around 11.30am on Tuesday 22 December following the sudden death of a 50-year-old woman.
“Her next of kin have been made aware.
“There are no suspicious circumstances and a report will be submitted to the Procurator Fiscal.”
In 1993, aged 23, Tennant broke into modelling, posing for magazines such as French, British and Italian Vogue as well as Harper’s Bazaar.
In the late 90s, Karl Lagerfeld announced Tennant as the new face of Chanel,.
She appeared in numerous advertising campaigns, including Calvin Klein, Chanel, Hermes, and Burberry.
In 2012, Tennant was inducted in the Scottish Fashion Awards Hall of Fame.