Hobson was dispatched from London in August 1839 with instructions to take the constitutional steps needed to establish a British colony in New Zealand. He was sworn in as Lieutenant-Governor in Sydney (under George Gipps) and arrived in New Zealand on 29 January 1840. On 5 February 1840, Hobson met with Māori chiefs at Waitangi, where they signed a treaty by which the chiefs voluntarily transferred sovereignty to the British Crown in return for guarantees respecting their lands and possessions and their rights as British subjects. Three months later, Hobson proclaimed British sovereignty over the islands of New Zealand. He also selected the site for a capital in the North Island, which he named Auckland.
In May 1841, New Zealand was constituted as a separate Crown colony, with Hobson promoted to Governor and Commander in Chief. In his final months Hobson was dogged by poor health which left him detached from political affairs. He died in office in September 1842.
He joined the Royal Navy on 25 August 1803 as a second-class volunteer. He served in the Napoleonic wars and was later involved in the suppression of piracy in the Caribbean. He became a midshipman in 1806 and some seven years later was a first lieutenant. He was promoted to commander in May 1824 and commanded HMS Scylla between 1826 and 1828. In December 1834, he obtained a commission from Lord Auckland to the East Indies on HMS Rattlesnake.
In 1836, he was ordered to Australia, arriving at Hobart on 5 August 1836 and at Sydney 18 days later. On 18 September 1836, HMS Rattlesnake left for Port Phillip District (later Melbourne) conveying Captain Lonsdale and other officials to the new colony. During the next three months, Hobson and his officers thoroughly surveyed Port Phillip, the northern portion of which, by direction of Governor Sir Richard Bourke, was named Hobsons Bay, after him. His ship was involved in the founding of Williamstown. He was offered the position of Superintendent of the Bombay Marine at a salary of £2000 a year, but he had taken a liking to Australia and was a candidate for the governorship of Port Phillip, although the salary was not expected to be more than £800 a year.