Scott, a former model whose slim-fitting dresses were favorites 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," said New York police Detective Kelly Ort.
Police said they had preliminary information that Scott was 49, although that had not been confirmed by her family.
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 6-foot, 3-inch (191-cm) tall, raven-haired Scott towering over her rock-star boyfriend.
The news of Scott's death stunned friends, clients and fellow designers. Kidman, a friend of 25 years, was "heartbroken and in shock right now and unable to say anything," her spokeswoman said.
Her death followed the untimely deaths of two giants in fashion who succumbed to suicide: British designer Alexander McQueen, who had suffered from depression, died in London in February 2010 at the age of 40; his close friend, British fashion editor Isabella Blow, died in 2007 at the age of 48.
Scott became one of New York's most famous designers over the last decade, with a sensibility that catered to women's desire to feel powerful and sleek.
"L'Wren was a total perfectionist, someone who absolutely embodied everything her marvelous clothes stood for: strength of character combined with a confident and powerful style," long-time Vogue magazine editor Anna Wintour wrote on Vogue.com.
It was unclear if Scott had shown any signs in her work or personal life that foreshadowed her death.
A publicist for Jagger said a New York Post story about a split between the two "is 100 percent untrue" and "a horrible and inaccurate piece of gossip during this very tragic time for Mick."
Fashion, music worlds grieve
Police said a woman was found "unconscious and unresponsive" in an apartment building in the upscale Chelsea neighborhood. Fire officials, who responded to a cardiac arrest call, said the woman was dead when they arrived.
Julie Bolcer, 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. Foul play was not suspected, police said.
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 a swarm of media gathered across the street.
The Rolling Stones are on tour, currently in Perth, Australia. It was not known whether they would cancel their concert there, scheduled for Wednesday.
Musician and fashion friends of the couple took to Twitter to express their grief.
"Devastated to have lost my friend," tweeted rocker Bryan Adams, who has photographed Scott. "Rest in peace my dear I'm gonna miss you. Condolences to all that were close to her."
Jagger's first wife, Bianca, said she was "heartbroken to learn of the loss of the lovely and talented L'Wren Scott. My thoughts and prayers are with her family."
American fashion designer Marc Jacobs said: "You'll forever be missed."
Knowing what women want
Scott, born Luann Bambrough, was raised in Utah by adoptive parents. She 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.
"She pushed aside interest in what was happening in fashion trends and on the runways, and designed for women, to give them confidence with their bodies in looks that were so beautiful," said Eric Wilson, the fashion news director at InStyle magazine.
Her styling background proved important to who she was as a designer and she was constantly shopping for the women she dressed.
"That experience gave her an incredible amount of ammunition when she started designing her own clothes. She knew what worked best for all body types," Wilson said.
She canceled a planned show for her fashion label at London Fashion Week last month.
The last collection that she showed, in September 2013, 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 collaborated with many in the fashion and beauty industry, including Lancome for her first makeup collection, and designed Italian-made shoes, handbags and eyewear, and a small holiday collection for Banana Republic last year.