Tests included reaction speed, logical problem solving, and multiple different tests of memory.
The study from the NICM Health Research Institute and Western Sydney University showed the relationships were consistently strong in both people aged under 55 and those aged over 55.
"When taking multiple factors into account such as age, gender, bodyweight and education, our study confirms that people who are stronger do indeed tend to have better functioning brains," said researcher Joseph Firth.
He said: "We can see there is a clear connection between muscular strength and brain health. But really, what we need now, are more studies to test if we can actually make our brains healthier by doing things which make our muscles stronger - such as weight training."
The findings are published in Schizophrenia Bulletin. (ANI)