Scientists used data from NASA's Lunar Prospector mission collected in the late 1990s and spotted two hydrogen-rich regions near the Moon's poles, probably indicating the presence of water ice.
The icy patches are opposite each other - the line between them passes through the middle of the Moon - so it appears that this used to be its spin axis, 'BBC News' reported.
According to Matt Siegler, from the Planetary Science Institute in Arizona, and his colleagues, it describes a gradual wobble, or "true polar wander", adding up to about a six-degree shift altogether.
This swathe of territory includes most of the Moon's dark patches that are visible from the Earth. Volcanoes and associated geological activity would have made it warmer and lighter than the rest of the Moon, they said.
Drop in density produced enough wobble to explain the two "palaeopoles" researchers detected in the Lunar Prospector data, they said.
"The Procellarum region was most geologically active early in lunar history, which implies that polar wander initiated billions of years ago," researchers wrote in the journal Nature.