He attended Brisbane Grammar School and the University of Queensland where he gained honours, masters and doctoral degrees in English and taught for nine years.

Literary influences he has mentioned include W. H. Auden, Billy Collins, Elizabeth Bishop, Franz Kafka, Simon Armitage, Sharon Olds, John Berryman, Carolyn Forché and Judith Wright.

Edward Britton , a young adult novel co-authored with Gary Crew was a CBC Australian Notable Book in 2001.

Neilsen’s poetry has been acclaimed by Les Murray, John Kinsella, Sarah Holland-Batt, Bronwyn Lea, Martin Duwell and Bruce Dawe, among others.

His book "Wildlife of Berlin" was shortlisted for the Kenneth Slessor Poetry Prize in the New South Wales Premier's Literary Awards, 2019.

His areas of research include creative writing therapy in the promotion of mental health, eco-criticism, and environmental poetry.

The Art of Lying (Makar Press, 1979) Australian Poets on Tape: Philip Roberts & Philip Neilsen (UQP, 1980) Life Movies (QCP, 1981) We’ll All Go Together (with Barry O’Donohue)(QCP, 1983) Without an Alibi (Salt: Cambridge, 2008) Wildlife of Berlin (University of Western Australia Publishing, 2018) Emma and the Megahero (Reed Books, 1995) The Lie (Lothian, 1997) The Wombat King, (Lothian, 1997) Edward Britton (with Gary Crew) (Lothian, 2000) Splot the Viking (Penguin, 2008) Imagined Lives: A Study of David Malouf (University of Queensland Press, 1990 & revised 1996) The Cambridge Companion to Creative Writing Co-edited with David Morley (Cambridge University Press, 2013) Creative Arts in Counseling and Mental Health Co-edited with Robert King and Felicity Baker (SAGE, 2015) The Penguin Book of Australian Satirical Verse Edited by Philip Neilsen (Penguin Books, 1986) The Sting in the Wattle Edited by Philip Neilsen (University of Queensland Press, 1993) 50 Years of Queensland Poetry Co-edited with Helen Horton (Central Queensland University Press, 1998) Difficult Love: Short Stories Co-edited with Helen Horton (Central Queensland University Press, 2000) His short stories have appeared in The State of the Art (ed.