Müller was born in the canton of Aargau, Switzerland, probably in the village of Oftringen. He grew up to become a compositor and type-setter in the town of Aarau. At the age of nearly thirty, in July 1857, he left Aarau and set off for Australia on board the 'Helvetia'. His adventures in Australia are recounted in his book, Neunzehn Jahre in Australien, published in Switzerland one year after his return.
The 'Helvetia' arrived at Port Jackson on 5th December 1857. Müller was unable to find work in Sydney, and travelled to the Hunter Valley, then to the Paterson river. He worked as a gardener at Dunmore from 1858 to 1859, then travelled north to the Manning River, where he worked as a shepherd for Isabella Kelly (q.v.) for some months. After leaving this position he worked in many settlements in the New South Wales hinterland, and made a failed attempt to stake a claim at the Louisa gold mines. In May 1862 he returned to Sydney, and gained work as a compositor for the newly-launched weekly Der Heimathsbote. When the paper ceased in 1863, Müller left Sydney again. He worked on a farm at Coolac near Gundagai until 1870, and then moved to Brisbane. Again he worked on the land, remaining in Brisbane until 1876. He departed Australia from Sydney on 26 February 1876 on the 'St.Osyth', and in May of that year he arrived home in Aarau.
The Swiss Theodor Müller is not to be confused with the German Theodor Müller (q.v.), who also travelled in Australia in the mid-nineteenth century. Augustin Lodewyckx, in his Die Deutschen in Australien (1932), mixed up the two, and many library catalogs have since repeated the error.
Major source : John Fletcher 'Theodor Müller and his Nineteen Years in Australia', Antipodische Aufklarungen = Antipodean Enlightenments, herausgegeben von Walter Veit (1987) 87-104.