Neilson was born in New Brunswick, Canada and trained in Dalhousie University Faculty of Medicine, followed by Memorial University of Newfoundland. He currently has a medical practice in Erin, and lives with his family in Guelph, Ontario.
His book, Call me Doctor, published in 2006, is an autobiographical account of his medical experiences. His books of poetry include Complete Physical, Meniscus and Exterminate My Heart. In 2010, Neilson won Arc Poetry Magazine’s 15th annual Poem of the Year contest.
In addition to being an author, Neilson is a notable critic and the poetry editor for Frog Hollow Press, and in 2005 he was editor for a collection of Alden Nowlan’s medical poems called Alden Nowlan and Illness.