Eleanor was the daughter of Murdoch Luke, a minister in the United Free Church of Scotland, and his wife Rose. Born in Stirling, Scotland, she grew up in Dundee and Arbroath. When she was twelve her family moved to Australia and settled in Woodville, SA. Her father died suddenly 16 months later, and the family moved to the newer suburb of Warradale.
Eleanor studied at the University of Adelaide and Adelaide Teachers' College concurrently, gaining a BA Hons and a DipEd. She taught at Plympton High School 1960-61 and then at Adelaide Teachers' College 1962-8. Here she met her husband, Neil. They were married in 1967 and moved to Coromandel Valley. She taught at the SA College of Advanced Education 1971-90 and University of SA 1991-2.
Eleanor had written stories as a child, most of them with tragic endings, but she didn't take up serious writing until she heard Jane Gardam, in Writers' Week, 1982, tell how she hadn't begun writing until she was middle-aged. Since that time Nilsson has written prodigiously. She has been a full-time writer since 1992 . As well as the fiction listed below, she has written a handbook for authors of children's stories, Writing for Children (1992). She was awarded Fellowships from the Literature Board of the Australia Council, Category B 1988, Category A 1993. She is married, with 2 children.