Webber, whose 1776 portrait of Captain Cook is now held in the Museum of New Zealand Te Papa Tongarewa, captured the dramatic moment of his death in the 29.5 x 40cm image, published in July 1785.
Now, a "very good copy" of the famous impression is going under the hammer at Cordy's Auction House in Auckland.
"It was not engraved in time for the publication of the accompanying atlas to the voyage for the British Admiralty and was thus issued separately," said Cordy's director Andrew Grigg.
"It is considered an integral part of any collection specialising in South Sea and Cook material."
The image will go under the hammer with an estimate of $8000-$12,000 on March 15.