James Cook was never Governor of New South Wales. All he did was to chart the eastern coast, claim it for England and name it New South Wales. He died before the First Fleet was even considered, let alone established and sent to NSW.
Captain Arthur Phillip commanded the First Fleet. He was a naval officer who, in October 1786, was appointed Governor-designate of the proposed British penal colony of New South Wales.
Lieutenant James Cook claimed the eastern seaboard of Australia in 1770, naming it New South Wales. The First Fleet of English convicts, together with officers, marines and their families, arrived in 1788.
The first planned "migration" of European settlers to Australia occurred with the First Fleet of convicts, officers and marines, with a few free settlers among the marines' families. The First Fleet left England in May 1787 and arrived in Australia in January 1788.
Sydney.The first convicts were sent to New South Wales to colonise Botany Bay, but Botany Bay proved unsuitable, so the fleet moved north to Port jackson, where Sydney now stands.
Australia was originally settled as a penal colony. English convicts, together with officers and marines, were sent on the First Fleet to New South Wales in 1788.See also the related question.
194 Ships in the blockade fleet.
Australia was colonised by British prisoners. The British government sent a fleet of convicts and officers, under the command of Captain Arthur Phillip, to colonise the land that James Cook had named and claimed as "New South Wales".
On 18 August 1786 the decision was made to send a colonisation party of convicts, military and civilian personnel to Botany Bay, under the command of Captain Arthur Phillip, who was appointed Governor-designate.
It was not a single ship, but a fleet consisting of eleven ships. It was called the First Fleet.
The First Fleet of ships carrying convicts to Australia departed Portsmouth, England on 13 May 1787.
The First Fleet, carrying convicts, officers, marines, and their families, landed in Botany Bay on 18 January 1788, but did not disembark. The Fleet then landed in Port Jackson, where Sydney is now located, on 26 January 1788, to establish a convict colony.