Rocketing to fame as a teenager in the 1990s when she appeared in British Vogue magazine, she had a long and successful career, working as a catwalk model and face of campaigns for Chanel, Valentino and Versace.
She appeared at the closing ceremony of the 2012 London Olympics along with fellow models Naomi Campbell and Kate Moss.
Her death prompted tributes from top designers including Stella McCartney, who said it was "sad, horrific news".
British Vogue described her as "one of fashion's most beloved and idiosyncratic personalities" and a "groundbreaking figure in the history of British style".
Tennant was the grand-daughter of Deborah Mitford, the Duchess of Devonshire, who died in 2014.
The model was married to French photographer-turned-osteopath David Lasnet and the couple had four children.