Following the late designer’s funeral on Tuesday, L’Wren’s brother confirmed the cremation, saying : "She was cremated and I have some of her ashes."
The 49-year-old took her own life on 17 March. She was found dead in her eighth floor apartment in New York City by her assistant.
The ceremony on Tuesday was a small, private affair with only 70 friends and family.
Randall, speaking to the New York Daily News, said: '"Some of those ashes, they will be buried near our parents here in Utah. And there will be a ceremony, date to be determined, in Utah for all family members who will have an opportunity to see their friends and others."
He admitted he did not know what the Jagger family intended to do with the ashes they received, saying: "They're with the Jagger family. That's all I can say."
Earlier this week it was reported that L’Wren left her entire $9million fortune to boyfriend Mick Jagger.
A simple will, it supposedly stated that all her personal effects, including clothing, jewellery, cars and furniture were to be left to "Michael Phillip Jagger".
The Rolling Stones frontman was on tour in Australia when the news of his partner’s death broke.
L'Wren Scott and Mick Jagger
"I am still struggling to understand how my lover and best friend could end her life in this tragic way," the Rolling Stones band member wrote on his website in a post titled 'L'Wren'.
"We spent many wonderful years together and had made a great life for ourselves", he added before continuing, "She had great presence and her talent was much admired, not least by me.
"I have been touched by the tributes that people have paid to her, and also the personal messages of support that I have received."
Concluding, he said, "I will never forget her."