The designer, who committed suicide earlier this month, willed property and other items totaling more than $9 million in value to the 70-year-old Rolling Stones frontman, whom she was dating for more than 12 years, the Associated Press reported.
The New York Post's Page Six column cited documents filed in Manhattan's Surrogate's Court on Wednesday and posted them on its website.
"I give all my jewelry, clothing, household furniture and furnishings, personal automobiles and other tangible articles of a personal nature ... to Michael Philip Jagger," Scott wrote in the documents.
"Except if otherwise provided in this will, I have intentionally omitted to provide herein for any of my heirs living at the date of my death," added the 6-foot-4 designer, who had a brother and a sister.
The documents were reportedly signed in Beverly Hills in May 2013, the paper said.
According to court documents, her estate includes her $8-million condo in Chelsea, where she was discovered hanged on March 17, and other items estimated to be worth $1 million. Jagger's net worth has been estimated at $328 million.
Scott, who was 49 when she died, was mourned by Jagger and other family and friends at the Hollywood Forever Cemetery in Los Angeles during her funeral service on Tuesday.
The former model, born Laura "Luann" Bambrough, was cremated, per her wishes, and her ashes will be split between her family and Jagger, the New York Daily News reported.
"She was cremated and I have some of her ashes,” said her brother, Randall Bambrough, who was appointed director of her fashion house in November. "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.”
Jagger is said to be in possession of the rest of the ashes, though Bambrough said he doesn't know what he plans to do with them.
Meanwhile, the L’Wren Scott Amber Award has been created by the Art of Elysium, which brings art to hospitalized children. The award, which honors emerging fashion designers, was named after Scott and a young girl named Amber who had a brain tumor.
Follow Ministry of Gossip @LATcelebs.