The 53 months is the longest known egg-brooding period for any animal species, they wrote in the scientific journal PLOS ONE.
"It's extraordinary. It's amazing. We're still astonished ourselves by what we saw," said Bruce Robison, a deep sea ecologist at the Monterey Bay Aquarium Research Institute in Moss Landing, California.
The octopus species, called Graneledone boreopacifica, dwells almost a mile below the sea surface in the dark and frigid depths of the Pacific Ocean.
They tracked one female, recognisable by its distinctive scars, that clung to a vertical rock face near the floor of a canyon about 4,600ft (1,400 metres) under the surface, keeping the roughly 160 translucent eggs free of debris and silt and chasing off predators.
The octopus never left the oblong-shaped eggs - which during the brooding period grew from about the size of a blueberry to the size of a grape - and was never seen eating anything.
The octopus progressively lost weight and its skin became pale and loose.
The researchers monitored the octopus during 18 dives over 53 months from May 2007 to September 2011.
The species is about 16in (40 cm) long and is a pale purple colour with a mottled skin texture. It eats crabs, shrimp and snails.
The scientists used a remote-controlled submarine to monitor the deep-sea species, off the coast of central California.
Most octopus females lay a single set of eggs in a lifetime and die shortly after their offspring hatch.
The long brooding period enables the hatchlings to come out of their eggs uniquely capable of survival, emerging as fully developed miniature adults able to capture small prey.