Born in Yorkshire, England, he came to New Zealand in the early 1850's amd settled in Auckland where he bagan making bricks and also took a one third interest in a flour mill. In 1859 he made his first visit to Mata Mata where he met and became friendly with Wiremu Tamehana, the King Maker.
In 1865 in the aftermath of the Invasion of the Waikato, Firth was able to lease from Tamehana a large area of land around Mata Mata for a rental of five hundred pound a year. Two years later he bought outright some of the land covered by the lease and this became the basis of his estate at Mata Mata. Meanwhile his businesses in Auckland were prospering and he was able to build himself a very fine house on the eastern side of Mt Eden.
Early in 1870 Josiah, or Hohaia as he was known to the Maori, was contacted by Te Kooti during his flight from Te Porere through the King Country and back to the Ureweras. Te Kooti wanted Hohaia to negotiate on his behalf with the New Zealand Government.
In 1873 Firth began a seven year project to clear the Waihou River of snags and obstacles to navigation thus opening the upper reaches of the Thames Estuary to shipping.
New Zealand agriculture went through a serious depression during the 1880's, one which hit Firth hard, and in 1889 he was declared bankrupt. Later he bagan to develop a trade in pumice based on its properties of insulation and fire resistance, travelling to the USA and England. However he died suddenly just as the venture was becoming successful.