"The world we face right now is a weight on many shoulders, including those in the arts who have had their livelihoods heavily impacted by Covid lockdowns."
The family described the 33-year-old as an "overwhelmingly kind and caring" person.
The Sydney resident leaves behind his long-term partner Lachlan, his mother May, his father Reginald, and his younger brothers Jeremy and Laurence.
"We are devastated by the loss of our beloved Francis Mossman," the statement began.
Didn't see you as often as we'd like, but we'll remember the energy, laughs, and genuine excitement when we were together. Love you, big bro.
Posted by Laurence Mossman on Sunday, August 15, 2021
"Francis was overwhelmingly kind, enthusiastic and so very caring, making a positive impact on the lives of many who knew him.
"He had the most infectious smile along with the most brilliant sense of humour imaginable. He was forever a big kid and with that he had the warmest most generous loving heart that lit up wherever he went.
The family added the actor will be "loved dearly and equally missed".
"Recently, he took to social media to fondly remember childhood vacations as some of his happiest memories as well as his undying love for all things Gillian Anderson."
The family thanked "those who loved and admired Francis for their kind words of love and support" and asked for privacy.
On August 4, the star uploaded several photos of himself in bed with his Cavoodle puppy Piper.
"Pup isn't loving lockdown..." he wrote.
Prior to that he posted another photo of himself looking unimpressed, saying "Me being excited for at least four more weeks of lockdown."
Mossman had lost his beloved 5-year-old dog, Hoff, back in May.
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youthline: 0800 376 633 or text 234 (available 24/7)
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (12pm to 11pm)
• Depression helpline: 0800 111 757 or text 4202 (available 24/7)
• Anxiety helpline: 0800 269 4389 (0800 ANXIETY) (available 24/7)
• Rainbow Youth: (09) 376 4155
If it is an emergency and you feel like you or someone else is at risk, call 111.