It was named in 1770 by explorer James Cook, after his own vessel, HMS Endeavour, and he used the strait as passage out to the Indian Ocean on his voyage.

The strait is, on average, between 13 and 15 metres (7 and 8 fathoms) deep, and its sandy floor is carpeted with a moderately thick layer of coral.

[3] The strait is generally safe to travel through, and is not littered with any major sunken dangers or foul ground,[3] although, for larger vessels, there is potential danger at the strait's western end, at the point that it connects with the Arafura Sea, where the depth of the water is only around 5.5 metres (3 fathoms).

If they had been able to pass through the Endeavour Strait at the time, it is likely they would have discovered eastern Australia approximately one hundred and fifty years before the British did,[4] in 1770, as the Dutch had been successful in mapping most of the west coast of Australia during the early 17th century following Willem Janszoon's sighting of the Cape York Peninsula in 1606.

[5] Today, the strait is travelled sparsely by passing small vessels, and its western side is often used as a bank for these ships.