He was born on 12 October 1869, in East Maitland, New South Wales, to William Dwyer, school inspector, and his wife Anastasia Dermody.
[2] He returned to Australia to become Professor at St. Patrick’s College in Goulburn, New South Wales, where he developed a keen interest in botany.
Dwyer's red gum, Eucalyptus dwyeri]] was named in his honour by Joseph Maiden and William Blakely.
[5] In 1920, Dwyer attracted attention when he secured the arrest of an "escaped nun", Sister Liguori, on the grounds that she was insane.
With the support of the Orange Order, she sued Dwyer for £5000 for wrongful arrest and mistreatment.