It was the Englishman Captain James Cook who became the first
European to explore the east coast. When he sailed west around
Cape Horn into the Pacific on the Endeavour, in the wake of
Magellan, he sailed first to New Zealand which he charted
properly. He then sailed on in search of the east coast of the
"Great South Land" that had been seen by the Dutch and
Dampier and others.
On 20 April, 1770, Cook's crew member Lt. Zachary Hicks
finally sighted the east coast of Australia that had been
eluding navigators since Magellan had sailed cross the Pacific
much further to the north in 1519 - 250 years earlier.
Cook charted the east coast of the continent and took
possession of it in the name of the English King.
Although Cook's Endeavour was damaged on the way back to
England, he still managed to return safely and give good reports
about the east coast that led to settlement.