TV host Sharon, 69, said of the 38-year-old: "Today my daughter Aimee was working in a recording studio at this building with her producer.
"They are the lucky two who made it out alive. It is utterly heartbreaking someone lost their life in this fire. What happened today was beyond horrific."
The producer and musician Aimee, daughter of rock star Ozzy, 73, suffered smoke inhalation.
A team of 78 firefighters took an hour to put out the blaze in Hollywood on Thursday, which fire captain Erik Scott called "very challenging".
Aimee’s producer also escaped the blaze in the two story commercial building that houses several studios and music-making spaces.
Two people reported respiratory symptoms related to smoke exposure and were evaluated at the scene, but both declined to be taken to a hospital, Mr Scott said.
“Sadly, one person was found dead inside, as firefighters searched the structure,” Mr Scott said, adding that no firefighters were injured and the cause of the fire is under investigation.
Aimee Osbourne is a singer who releases electronic pop music under the name ARO, her initials.
She did not take part in the Osbourne family’s reality show as her younger siblings Kelly and Jack Osbourne did.
Davis, whose stage name is Jamal Rajad, both lives and works in his space in the building with his wife and four cats.
He thought his wife was burning incense when he began to see and smell smoke.