The 49-year-old model and designer had been dating the Rolling Stones frontman since 2001 following his split from wife Jerry Hall.
Her body was discovered yesterday by police "unconscious and unresponsive" in an apartment building in Manhattan's upscale Chelsea area. The high-rise building where Scott lived was cordoned off. Police believe it was an apparent suicide.
A spokesman for Sir Mick, who was in Australia for a concert, said: "He is completely shocked and devastated by the news."
The Rolling Stones yesterday flew to Australia for a concert.
Scott designed stage outfits for notable performances at Glastonbury Festival and Hyde Park in recent years. Sir Mick was there to support her when Scott showcased her collection in her debut London fashion show last year.
Tributes from the world of fashion and showbusiness flooded on to Twitter.
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."
Fashion designer Marc Jacobs wrote: "Rest in peace, L'Wren Scott. You'll forever be missed."
Pop band Duran Duran added: "Such sad news. Our condolences are with L'Wren's family and friends."
Entertainer Bette Midler wrote: "Just got news of the beautiful L'wren Scott's death perhaps by her own hand. I am devastated. A rare, wonderful, talented soul. Goodbye."
Actress Emmy Rossum tweeted: "So sad to hear of the death of L'Wren Scott. What a beautiful woman and an incredible designer".
Scott, who was born Luann Bambrough, was brought up in Utah as a Mormon by her adoptive parents.
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 was 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.
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."
A New York City Police Department spokeswoman said: "A 49-year-old female was found this morning at 10.05am at 200 11th Avenue. She was unconscious. She was pronounced dead on arrival by the emergency medical services. The investigation is ongoing. We are awaiting medical examiners to determine the cause of death."