Writing in the journal Science, they conclude that the hole has shifted wind and rainfall patterns right across the Southern Hemisphere, even the tropics.
Their climate models suggest the effect has been notably strong over Australia.
Many parts of the country have seen drought in recent years, with cities forced to invest in technologies such as desalination, and farms closing.
The scientists behind the new study - led from Columbia University in New York - added the ozone hole into standard climate models to investigate how it might have affected winds and rains.
"The ozone hole results in a southward shift of the high-latitude circulation - and the whole tropical circulation shifts southwards too," explained Columbia's Sarah Kang.
Of particular interest was the southward migration of the Southern Hemisphere jet stream.
These high-altitude winds are key to determining weather patterns, in both hemispheres. Much of the cold weather felt in the UK over the last couple of winters, for example, was caused by blocking of the Northern Hemisphere stream.
The Columbia team found that overall, the ozone hole has resulted in rainfall moving south along with the winds. (read more)