Nicholas Hasluck will be the next chair of the Art Gallery of WA board.
"Fiona has been an invaluable member of the Art Gallery board and will leave a lasting legacy in her contribution to the success of this highly respected institution," Mr Day said.
Mr Hasluck was appointed as a judge in the Supreme Court of Western Australia in 2000, and retired in 2010.
He is a well-known Perth writer whose novel The Country Without Music won the Western Australian Premier's Book Award in 1991. Mr Hasluck is a former chair of the Literature Board of the Australia Council.
His father, Paul Hasluck, was a minister in the Menzies federal government, and was later made Governor-General of Australia.
"As a retired Supreme Court judge and a well-known author, Mr Hasluck is well placed to bring his experience and personal interest in the arts to the state's flagship art gallery," Mr Day said.