Browne was born in Aylesbury, Buckinghamshire, England. He served with the British Army in Afghanistan, before retiring from the military in 1851 to become the Governor of St Helena.
In 1854 he was appointed to be the next Governor of New Zealand. He took up the position at the end of 1855. Overall he undertook the duties well, however he did not handle relations with the Maori particularly well. His handling of Maori affairs is seen by some as a contributing cause of the Maori wars.
The town of Gore in New Zealand was named after him.
From 1861 until 1868 he was Governor of Tasmania.
From September 1870 to April 1871 he was Governor of Bermuda.