His publicist said Perry died surrounded by his family and friends.
Perry rose to fame on Beverly Hills, 90210 and had been starring as Fred Andrews on the CW show Riverdale.
He was taken to hospital on Wednesday in Los Angeles, where he had been shooting scenes for Riverdale at the Warner Bros film lot.
Perry's children, Jack and Sophie, fiancée Wendy Madison Bauer, ex-wife Minnie Sharp, mother Ann Bennett, step-father Steve Bennett, and his siblings, Tom Perry and Amy Coder, were with him when he passed, publicist Arnold Robinson said in a statement.
"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," Mr Robinson said.
The family has not provided additional details at this time.
Last Wednesday, US media reported that paramedics had been called to the actor's home in Sherman Oaks.
Perry, a native of Ohio, was famous for starring in Beverly Hills 90210 from 1990 to 2000. A reboot of the series was also announced on Wednesday, though it was not clear whether Perry planned to make any guest appearances.
Former 90210 co-star Shannen Doherty - who played Perry's love interest on the show - told Entertainment Tonight on Sunday in an emotional interview that she had been in touch with him after his stroke.
"I can't talk about it here 'cause I will literally start crying but I love him and he knows I love him. It's Luke, and he's my Dylan."
Perry also starred in television show Oz, as well as films including Buffy the Vampire Slayer, 8 Seconds and The Fifth Element.
His most recent role was on the hit television teen drama series Riverdale, based on the Archie comics, where he played the titular character's father.