Who ordered Captain Cook to come to Australia?

Answer 1

James Cook was commissioned by the Royal Society in England to search the southern seas and find the "Great Southland" ("Terra Australis") that was believed to exist in the world's southern oceans somewhere. The result was that although he hadn't been the first European to discover Australia, he was the first known to have sailed along and chart most of the eastern coast of Australia - which was eventually to become the most significant for settlement.

Answer 2

James Cook was not a captain when he first came to Australia, but a Lieutenant. He was only promoted after his successful exploration,

Cook was originally sent on a scientific expedition to observe the transit of Venus from the vantage point of Tahiti in the South Pacific. Before he departed England, he was handed secret, sealed orders by the Royal Society in England to search the southern seas and find the "Great South Land" ("Terra Australis") that was believed to exist in the world's southern oceans. The Dutch had already explored much of the western coast, naming it New Holland, but whether or not it was part of an entire continent had not yet been ascertained. Cook was ordered to sail west from Tahiti and claim any unclaimed lands for Great Britain. He first came across New Zealand, then sailed further west and found the eastern coast of the continent now known as Australia. His next task was to make extensive notes and observations, and determine its suitability for settlement and colonisation.