"Thank you all for your love and kind words about Alexis. My hero for eternity," David added on the social media site alongside a black and white photo of himself posing next to his sister.
Cox and David were previously married for 14 years. Their divorce was finalized back in 2013.
My heart goes out to anyone who was lucky enough to know Alexis.— Courteney Cox (@CourteneyCox) September 11, 2016
We will love and miss you forever.
Alexis died Sunday with the cause of death yet to be disclosed. The transgender actress known for her roles in Last Exit to Brooklyn, The Wedding Singer and Blended, is also the sibling of stars Patricia Arquette, Richmond Arquette and Rosanna Arquette.