Moya Costello grew up in Sydney, and graduated with BA from the University of Sydney, 1973 and Dip Ed Sydney Teacher's College, 1973. She gained a Grad. Dip. Media Studies at the Victoria State College, 1983, completed an MA (Literary Studies) at Deakin University, 1996, and received her PhD from the University of Adelaide.

Costello lived in South Australia from 1984, and worked as a writer, editor and teacher. She was producer/editor of Author's Proof (1986-90) and has contributed to the Science Show (1989) and Arts Today (1994), as well as writing 14 episodes of the children's television program Here's Humphrey (1988-1990). She settled in Tasmania in late 2020, where she established a blog about eating and drinking locally. 

She was the author of two collections of short prose (Kites in Jakarta and Small Ecstasies), two novellas (Harriet Chandler and The Office as a Boat) and one collection of prose poems (Pressed Specimens).

Costello taught writing in TAFE, community-based groups and Continuing Education and university seminars fom 1982, and edited several anthologies arising from those classes.

She was a guest reader at events and venues around Australia from 1980 onwards, and was Writer-in-Residence at Monash University in 1996. She has also been an adjunct lecturer at Southern Cross University. She was on the judging panel (non-fiction) for the 1996 Adelaide Festival Awards for Literature, on the Writers' Week Committee for the 1998 Adelaide Festival, and a guest at the Sydney Writers' Festival in 2000.

She won a Literature Board grant in 1984, a South Australian Department of the Arts grant in 1987 and 1994, a Varuna Fellowship in 1994, and the Barbara Hanrahan Fellowship in 1996. Her collection of prose poems, Pressed Specimens, was highly commended for the 2022 Anne Elder Award and was nominated by the publisher for a Pushcart Prize.