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The Beverly Hills 90210 and RIverdale star was 52.
Perry's family issued a statement saying: "He was surrounded by his children Jack and Sophie, fiancé Wendy Madison Bauer, ex-wife Minnie Sharp, mother Ann Bennett, step-father Steve Bennett, brother Tom Perry, sister Amy Coder, and other close family and friends.
"The family appreciates the outpouring of support and prayers that have been extended to Luke from around the world, and respectfully request privacy in this time of great mourning. No further details will be released at this time."
Perry, who rose to fame in the 1990s for his role on the hit television series Beverly Hills 90210 was hospitalised in California after suffering a "massive" stroke at his home in Sherman Oaks last week.
The 52-year-old actor was rushed to a Los Angeles-area hospital where his condition reportedly worsened and he remains under observation.
Prior to his stroke Perry was said to be experiencing "bad back problems", which had to be surgically fixed, according to the actor's neighbour.
Perry's last major health scare was in 2015, when precancerous growths were found in his body following a colonoscopy, prompting the actor to speak out about checking for colorectal cancer.
His role as Dylan McKay on Beverly Hills 90210 made him one of TV's top heartthrobs of the 1990s.
Perry had been in Los Angeles working on the television series Riverdale, an adaptation of the Archie comic books in which he plays Archie's father Fred Andrews.
He played the onscreen father of Kiwi actor KJ Apa in Riverdale.
Perry was born in Mansfield, Ohio, on October 11, 1966, and grew up in nearby Fredericktown.