Thomas Herbert Wragg was born at Emu Bay, Tasmania on 6 November 1888, to parents Herbert Harnett and Annie Rebecca Wragg (nee Paice). He was educated at the State School in Somerset, Tasmania and worked as a labourer before the First World War. He married Leah Marion Powell in 1915, and they later had a daughter Rita Amy Rose.
Wragg enlisted in the Australian Imperial Force on 11 September 1915 and was assigned to the 26th Battalion. He departed Melbourne aboard HMAT Afric on 5 January 1916. After training in Egypt, Wragg joined his unit in France in early August 1916. He was wounded in action near Pozieres on 9 August 1916. His mother thought he had been killed in action, so he reassured her that was not the case in a postcard message.
Wragg re-joined his unit in early September 1916 and was still with the unit in October when thebattalion was again engaged in the Somme Valley. In late October, Wragg had been admitted to the field hospital for myalgia and again in early November for rheumatism. He was sent to the segregation camp in Etaples, before re-joining the battalion in February 1917. During May 1917, he was with the 26th battalion during their attempt to breach the German defences around Bullecourt. It was during this fighting that Thomas Herbert Wragg was killed in action on 3 May 1917 and is commemorated on the Villers-Bretonneux Memorial, France.