The 49-year-old's assistant found her hanged in her NYC apartment, the New York Daily News writes.
A press officer told HuffPost UK the New York Police Department had responded to a call at 10.05am on Monday to an 11th Avenue address where they found a 49-year-old woman unconscious and unresponsive.
The woman was later declared dead by emergency medical technicians. The press officer added a medical examiner will determine the cause of death pending family notification.
A spokesman for Jagger said the singer was "completely shocked and devastated" following the death of his girlfriend.
The Rolling Stones are currently on tour in Australia.
Scott, who was also a model, and Jagger had been dating since 2001, following his split from wife Jerry Hall.
A towering figure said to be 6ft 4ins tall, Scott became a household name in Britain after she got together with Jagger.
She designed stage outfits for notable performances at Glastonbury Festival and Hyde Park in recent years. Jagger was there to support her when Scott showcased her collection in her debut London fashion show last year.
An hour before the news broke, Scott's official Facebook page published this image.
Fellow fashion designer Marc Jacobs tweeted: "Rest in peace, L'Wren Scott. You'll forever be missed."
Bianca Jagger, one of Sir Mick's former loves, tweeted: "Heartbroken to learn of the loss of the lovely and talented L'Wren Scott. My thoughts and prayers are with her family. May she rest in peace."
A spokesman for the British Fashion Council said: "We are deeply saddened at the news of L'Wren Scott's tragic death.
"She was an iconic woman who inspired so many, and a designer whose contributions to the fashion industry were both extraordinary and unique.
"She will leave behind an exceptional legacy however we are so incredibly proud to have had her in our midst. At this sad time our thoughts are with her friends and family."
Scott, who was originally called Luann Bambrough but changed her name to launch her modelling career in her teens, was brought up in Utah as a Mormon.
She worked in Paris for a number of years, with the likes of Thierry Mugler and Karl Lagerfeld, then went on to return to the US as a stylist. The designer was a wardrobe consultant for films such as Eyes Wide Shut and Ocean's Thirteen.
She met Sir Mick, 70, when she worked as a stylist on a photo shoot. She launched her fashion line in 2006 with fans of her work said to include Sarah Jessica Parker, Nicole Kidman and Michelle Obama, and she had also designed for Banana Republic.
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