The 40-year-old mother-of-four was found dead in bed at her home in St Luke's Mews, Notting Hill, west London, on Sunday.
Several newspapers report that she was found by her four-year-old daughter Tiger Lily, who told a family friend on the phone that she was unable to wake her up.
Police have said they are treating the death as suspicious.
However, Detective Inspector Mike Christensen confirmed that Miss Yates had been alone in the house overnight and said there had been "no sign of violence or anything of that nature".
He added that her four daughters were being cared for.
Police have cordoned off the street around the house.
The body was removed from the house just before 1500BST and taken by private ambulance to Westminster Mortuary.
"
We are all so sad - the loss for all the children is insupportable
"
Bob Geldof
Miss Yates had three children with former husband, musician Bob Geldof - Fifi Trixibelle, 17, Peaches Honeyblossom, 11, and Pixie, 10.
The father of Heavenly Hiraani Tiger Lily, her fourth child, was Australian rock star Michael Hutchence, who died in a hotel room in Sydney in 1997.
Fifi Trixibelle visited her mother's house on Sunday night, laying a bunch of yellow roses by the steps.
Visibly affected, she went inside for five minutes to see the scene of her mother's death, escorted by a police inspector, and left with friends.
Bob Geldof said in a statement: "We are all so sad. The loss for all the children is insupportable."
Speaking of the family's "pain" at Paula's death, the statement added: "Leave them [the children] with their loss and Paula with her dignity."
'Terrible shock'
Paula's mother, Helene Thornton, speaking from her home in southern France, said she was "devastated" to learn of her daughter's death.
"This has come as a terrible shock to everyone. I am waiting for calls from London to find out exactly what has happened."
Mr Hutchence's father, Kell, expressed shock on hearing the news.
Speaking from his Sydney home, he said: "Of course we are in deep shock, we did not expect this at all. It is terribly tragic.
"We always supported and tried to get along with Paula.
"I feel so very sad for my little granddaughter Tiger Lily."