Bailey's body was discovered by his assistant at his Los Angeles home on Friday. Emergency services were called to the scene, but the 37-year-old could not be revived, reported TMZ.
Officials suspect he succumbed to carbon monoxide poisoning.
No further details about the tragedy have been released, but an autopsy is expected to be conducted by the LA County Coroner.
Bailey, who also worked as a photographer, was best known for his work with Gomez and Perry, and helped take care of the "Firework" singer's look for the 2015 Super Bowl Halftime Show in February.
"Shameless" star Emmy Rossum has taken to Twitter to mourn the loss of her friend.
"I am gutted to hear of my friend Jake's passing," she wrote.
"I saw him on Sunday, we flew together on a plane. He made me laugh as always."
Actress Octavia Spencer added, "My thoughts and prayers are with those who knew and loved #JakeBailey.
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