“My heart goes out to your stunning family who must be in such underserving pain.
“I am speechless… Rest in peace, you inspiring woman.
“Your soul and inner beauty exceeded the external perfection, Stella.”
The granddaughter of the 11th Duke of Devonshire, Andrew Cavendish, and Deborah Mitford, Tennant rose to fame in the 1990s, walking the runway for designers including Versace and Alexander McQueen.
She 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.