The cause of death was announced by the office of the medical examiner after Scott's body was discovered in her flat by her assistant on Monday.
Police earlier said there was no sign of foul play and no note was found.
Scott's long-term boyfriend, Sir Mick Jagger, postponed forthcoming Rolling Stones tour dates in Australia and New Zealand after her death was announced.
Sir Mick earlier said he failed "to understand how my lover and best friend could end her life in this tragic way".
He said they had spent "many wonderful years together".
On Wednesday, Jagger's bandmates also expressed their shock at the news of Scott's death.
Drummer Charlie Watts said supporting Jagger was the band's priority.
"Needless to say we are all completely shocked but our first thought is to support Mick at this awful time," he said.
"We intend to come back to Australia and New Zealand as soon as it proves possible."
Keith Richards said "no-one saw this coming" and that Jagger had "always been my soul brother and we love him".
"We're thick as thieves and we're all feeling for the man," he added.
Ronnie Wood said: "This is such terrible news and right now the important thing is that we are all pulling together to offer Mick our support and help him through this sad time.
"Without a doubt we intend to be back out on that stage as soon as we can."
Tributes have poured in for Scott, 49, with fans including supermodel Naomi Campbell, Vogue editor Anna Wintour and singer Madonna eulogising the fashion designer.
Wintour described Scott as "a total perfectionist... always unbelievably generous, gracious, kind and so much fun."
Scott was found in her Manhattan apartment by her assistant at 10:00 local time (14:00 GMT) on Monday.
She had sent her assistant a text message 90 minutes earlier asking her to come to the apartment, without specifying the reason why, the Associated Press news agency reported.
It has since emerged that the fashion label founded by Scott had been heavily in debt.
The death of fashion designer L'Wren Scott has been ruled suicide by hanging, New York City authorities say.