The Mannequin actor, who was in hospice care, was surrounded by his wife, children and mother, when he died at his Altadena, California, home at 10:47 p.m. on Saturday, his son, Tariq Taylor, told the Los Angeles Times.
His agent, Dede Binder, says Taylor died of cancer, according to the Associated Press.
On Friday, the family posted on the Emmy-nominated actor's Facebook page that his health had started to decline.
"It is with love and gratitude that we sorrowfully announce that our darling, amazingly brilliant and dynamic Meshach, the incredible father, husband, son and friend has begun his grand transition," they wrote.
"Our friends who know and love us, please offer your prayers for his peace and blazing light as he ascends to the heavens. Those who need to call the family please do. Those who desire to post memories, we are open and graciously accepting all gestures of peace. Love, the Taylor family."
Taylor got an Emmy nod for his portrayal of a lovable ex-convict surrounded by boisterous Southern belles on Designing Women from 1986 to 1993. Then he costarred for four seasons on Dave's World.
Other series included Buffalo Bill and Ned's Declassified School Survival Guide.
His movie roles included a flamboyant window dresser in the 1987 comedy-romance Mannequin. He also appeared in Damien: The Omen Part II.
Taylor guested on TV series including Criminal Minds, Hannah Montana and The Drew Carey Show.
Born in Boston, he began his career as a member of Chicago's Goodman Theatre.
Reporting by ASSOCIATED PRESS