"It's arguably the first oil painting of New Zealand," Fletcher said, explaining how it had been in a private family collection before the trust discovered it was coming up for sale.
"We only bought it in September from a London private dealer. The one family had owned it since 1773 and it's such a thrill to have it. It bookmarks New Zealand art as we're still buying emerging artists but this is at the very start," Fletcher said.
Art writer Hamish Keith was delighted with the purchase. "This is a major acquisition. It's absolutely marvellous," he said, adding that most Hodges works were in Canberra or London - the majority in the National Maritime Museum in Greenwich.
Art experts said the painting was in good condition and although it was unsigned, strong evidence existed to support Hodges as the artist.
He lived from 1744 until 1797 and was the Resolution's artist on the Pacific voyage, sailing into Fiordland's Dusky Sound in 1773 where the crew recovered from their difficult and long voyage and established an observatory to determine New Zealand's position on the globe.
Hodges' much bigger work, A View in Dusky Bay, New Zealand, is in the Auckland Art Gallery collection and it too was painted in 1773. But, unlike the small work, it has been here since 1961 when it was bought.
The Auckland gallery has only two Hodges paintings and senior curator Mary Kisler said the Fletcher acquisition could be the only one completed by the artist while in New Zealand, as others were completed after he left here.
"I certainly don't know of any other painting done in New Zealand by Hodges, and like Constable and other landscape painters, sketches such as this would have been invaluable for capturing colour and atmosphere. Most of his works in New Zealand were in the form of drawings," she said.
The Fletcher trust owns more than 550 art works worth about $3 million and is New Zealand's biggest corporate art collection.
Richard Thomson, International Art Centre director, said: "It's a fabulous acquisition for them. These just don't come on the market." He estimated a major work by Hodges would sell for more than $1 million.
• The Fabulous Fletcher Collection, Waikato Museum, from today.