Simpson and his Donkey, sometimes called The Man with the Donkey, depicted a medical orderly supporting a badly wounded Anzac soldier on the way down the Gallipoli hill to a medical post.
The painting by Kiwi soldier and artist Horace Moore-Jones showed New Zealand stretcher bearer, Waihi-born Dick Henderson.
Mr Henderson was a teacher in Auckland and lied about his age in order to join the army when he was 19.
Simpson and his Donkey will be auctioned at Parnell's International Art Centre on March 25, a month before the centenary of the ill-fated Gallipoli landing.
The painting also showed the bravery of Englishman John Simpson Kirkpatrick, who enlisted in the Australian Imperial Forces when World War I broke out.
"Simpson ignored the flak, and the rifle and machine gun bullets and was often heard whistling as he helped the often barely-conscious soldiers on his errands of mercy," the International Art Centre said
"He lasted less than a month. On May 19, a Turkish bullet struck him in the heart and he died instantly."
Mr Henderson took over when Mr Simpson was killed.
The International Art Centre said Moore-Jones was thought to have painted six versions of Simpson and his Donkey. The painting to be auctioned was the last in private hands.
Richard Thomson, International Art Centre director, said it was an extremely rare offering and "represented the heart" of the Anzac tradition.
A photograph taken by fellow Kiwi James Jackson provided a template for the painting.
The International Art Centre said next month's auction would also include other important works by World War I artists, such as John Weeks, Alfred Avery Forrester and Frank Barnes.
April 25 marks the centenary of the Gallipoli landings. On that day in 1915, thousands of New Zealanders and Australians stormed the Gallipoli Peninsula in present-day Turkey.
According to the Ministry for Culture and Heritage, at least 87,000 Ottoman soldiers and 44,000 Allied soldiers were killed in the eight-month campaign.
Among the dead were 2779 New Zealanders, about one-fifth of all those who landed on the peninsula.
By John Weekes of NZME. News Service
