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Scott, a former model whose slim-fitting, boldly printed dresses were favourites among Hollywood's A-list stars such as Nicole Kidman, Amy Adams and Penelope Cruz, was found hanging from a scarf.
"We are investigating it as a suicide," New York police Detective Kelly Ort said.
Jagger, 70, said through a spokesperson that he was "completely shocked and devastated. Scott's family issued a statement asking for privacy.
The glamorous pair had been dating since 2001 and were often seen at celebrity events, with the tall, leggy Scott towering over her rock-star boyfriend.
Police said a female was found "unconscious and unresponsive" in an apartment building in the upscale Chelsea neighbourhood. Fire officials, who responded to a cardiac arrest call, said the woman was dead when they arrived.
A single bouquet of yellow daffodils was placed in front of the glass-fronted, high-rise building where Scott lived. Police cordoned off its entrance as swarms of media gathered across the street.
Julie Bolder, of the city's Office of the Chief Medical Examiner, said the office had not received the body nor begun work to determine the manner of death.
"Given the timing, that individual will probably be examined tomorrow and if everything is straightforward, the cause and manner of death would be available by tomorrow," she said.
FASHION, MUSIC WORLDS STUNNED
Scott was the second major fashion designer to die unexpectedly in recent years. British designer Alexander McQueen, who had suffered from depression, committed suicide in London in February 2010 at the age of 40.
British fashion editor Isabella Blow also took her own life in 2007 at the age of 48.
Scott's death brought an outpouring of grief from celebrities who wore her designs or met Scott at social events. A spokeswoman for Kidman said she had been close friends with Scott for 25 years.
"Nicole is heartbroken and in shock right now and unable to say anything," the spokeswoman said in an email.
"Devastated to have lost my friend," tweeted rocker Bryan Adams. "Rest in peace my dear I'm gonna miss you. Condolences to all that were close to her."
Jagger's first wife, Bianca, also expressed her grief on Twitter.
"Heartbroken to learn of the loss of the lovely and talented L'Wren Scott. My thoughts and prayers are with her family," she posted.
American fashion designer Marc Jacobs said: "You'll forever be missed."
The British Fashion Council described Scott as a woman who inspired many.
"She will leave behind an exceptional legacy however we are so proud to have had her in our midst. At this sad time our thoughts are with her friends and family," it said in a statement.
Scott was known for her lean sexy designs, especially the tight-fitting dresses favored by actresses. She canceled a planned show for her fashion label at London Fashion Week last month and decided to give private, intimate presentations instead.
Her last collection was inspired by Japanese culture and featured embroidery and sleek lines: white below-the-knee dresses belted at the waist; red, black and white skirts, shorts and jackets; a bold yellow dress and pants.
Scott, born Luann Bambrough, was raised in Utah by adoptive parents. The dark-haired beauty started her career as a model in Paris before becoming a stylist and designer.
Her love of fashion began when she made her own clothes as a teenager, according to her website. As a model in Paris, Scott became more interested in making clothes than modeling them.
After moving to Los Angeles, she worked as a stylist and designed privately before creating her own collection.
Scott collaborated with many in the fashion and beauty industry, including Lancome for her first makeup collection, and designed Italian-made shoes, handbags, eyewear and a small holiday collection for Banana Republic last year.
Where to get help:
- Youth services: (06) 3555 906
- Youthline: 0800 376 633
- Whatsup: 0800 942 8787 (noon to midnight)
- Depression helpline: 0800 111 757 (24-hour service)
- Rainbow Youth: (09) 376 4155
If it is an emergency and you feel like you or someone else is at risk, call 111.