Taylor died from a terminal illness at his home near Los Angeles, Dede Binder told CNN.
"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," the family said in a statement.
Since Designing Women ended he has appeared in numerous television series, including In the Heat of the Night, Hannah Montana and All of Us, and most recently had a role in two episodes of Criminal Minds.
He was survived by his wife, children, grandchildren and mother.
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