The transgender actress died in the early hours of Sunday morning surrounded by her siblings, a niece and other loved ones, her brother Richmond wrote on Facebook.
The actor wrote that she passed away at 12.32am while listening to David Bowie's Starman.
Paying tribute to Arquette, he said: 'I am feeling immense gratitude to have been afforded the luxury of sharing life with him/her, for learning from Alexis, for being given the gift of being able to love him/her.'
He added: 'Thank you, Alexis, I love you and will love you always.'
But he didn't reveal the cause of death, but said that he is 'immensely grateful that it was fast and painless.'
Arquette, who was born Robert, but transitioned to a woman in 2006, had been battling an undisclosed illness, TMZ reports.
The actress, best known for the roles in Pulp Fiction and The Wedding Singer, was also a prominent transgender activist.
'She was in a coma for four days at Cedars and no one was allowed to see her except for family,' a source close to the Arquettes told Radar Online.
Arquette's other famous siblings - actors David, Patricia and Rosanna - have yet to comment.
R.I.P.
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Originally Posted by Saph
You're giving me a million reasons about a million reasons