Finniss was born at sea off the Cape of Good Hope, Southern Africa,[1] and lived in Madras, British India.

He was sent to Greenwich, England, for his education, and then entered the Royal Military College, Sandhurst, placing first of sixteen candidates at the entrance examination.

[1] In 1835, Finniss sold off his commission and, having been appointed assistant surveyor under surveyor-general Colonel William Light, arrived in South Australia in September 1836.

In the interim between the departure of Governor Young in December 1854 and the arrival of Sir Richard Graves McDonnell in June 1855, Finniss acted as administrator of the colony.

There were early difficulties between the two houses but Finniss, during the four months his ministry was in power, succeeded in passing measures to deal with waterworks for Adelaide and commence the first railway in South Australia.

Finniss chose a site, Escape Cliffs, near the mouth of the Adelaide River for the settlement, but his choice was much criticised.

[11] A month later, the Aboriginal people mounted another raiding party, spearing several horses, which led to a great deal of anger in the depot.

Dr. Francis Goldsmith, who, apart from his medical duties, had been appointed Protector of Aborigines, demanded a place in the party, but was ordered by Finniss to remain at the depot.

[12] In May 1865, a dissident party of seven men fled to Champion Bay, Western Australia, in a small boat dubbed the Forlorn Hope, and Finniss was eventually recalled.

He retired from the government service in 1881 and spent his leisure in preparing an interesting but rambling Constitutional History of South Australia (1886).

His eldest daughter, Fanny Lipson Finniss (later Morgan), was the first European girl born in South Australia, on 31 December 1836 or 1 January 1837.