The animal was named "hoodwinker" after its discovery after eluding researchers for so many years.
Marianne Nyegaard, a marine scientist who found and named the fish, told CNN she "nearly fell out of my chair" when she saw the pictures of the beached traveller.
"When the clear pictures came through, I thought there was no doubt," she said. "It's intriguing what made this fish cross the equator."
The hoodwinker is larger and sleeker than other species of sunfish, weighing up to two tonnes (2,000kg).
They reportedly favour more temperate waters, such as off the coast of Chile or New Zealand.
A different form of sunfish appeared twice off the west coast of Scotland in a week last September.
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