"We are heartbroken to share the passing of our brother and son, Nicholas Brendon. He passed in his sleep of natural causes," they wrote alongside photos of Brendon through the years.
"Most people know Nicky for his work as an actor and for the characters he brought to life over the years. In recent years Nicky has found his passion in painting and art.
Brendon rose to fame as Xander, the loyal best friend of Sarah Michelle Gellar's Buffy Summers and Willow Rosenberg, played by Alyson Hannigan, on Joss Whedon's cult series, which aired from 1997 to 2003.
Hannigan paid tribute by sharing a photo of the pair from the show, writing: "My Sweet Nicky, thank you for years of laughter, love and Dodgers. I will think of you every time I see a rocking chair. I love you. RIP."
After Buffy ended, Brendon had recurring roles as cyber expert Kevin Lynch on seven seasons of Criminal Minds and appeared on Private Practice.
He also starred in Kitchen Confidential and appeared in films including Psycho Beach Party, Big Gay Love, and Unholy.
Brendon was open about his health struggles, including a heart attack, and underwent two spinal surgeries for cauda equina syndrome, a rare condition that can affect movement as well as bladder and bowel function.
He had also been candid about past struggles with addiction and mental health.
His family said: "While it's no secret that Nicholas had struggles in the past, he was on medications and treatment to manage his diagnosis and he was optimistic about the future at the time of his passing.
"Our family asks for privacy during this time as we grieve his loss and celebrate the life of a man who lived with intensity, imagination, and heart. Thank you to everyone who has shown love and support."
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