The Meet Mr. McNulty star passed away on 19 May (11) after suffering heart failure, according to the Hollywood Reporter.
Avery's career spanned more than 50 years and one of her first major roles was playing Charlton Heston's onscreen wife in 1952 movie Ruby Gentry.
She is best remembered for starring opposite Ray Milland in hit sitcom Meet Mr. McNulty, while her other roles have included parts in Rawhide, Charlie's Angels and Perry Mason.
Avery was married to actor Don Taylor until their divorce in 1955. She is survived by two daughters.