The Emmy Award winner passed away aged 90 in Palm Desert, California, according to the Desert Sun publication.
He was the lead director of the sitcom I Love Lucy from 1952 to 1957, and later went on to helm Bewitched, starring his then-wife Elizabeth Montgomery.
Asher picked up four Emmy nominations for his work on Bewitched, before scooping the Best Director prize for the show in 1966.
Duke has taken to her Twitter.com page to remember Asher, who made her a star when he co-created The Patty Duke Show.
She writes, "The joy Bill Asher brought to the earth insures (sic) him all the joy in heaven. I was blessed to know him. Thank you Bill, I Love you!! RIP Bill Asher, creator of Patty Duke show, I love you."
A memorial for Asher has been scheduled for 29 September (12) at the Desert Springs Church in Palm Desert.