In the first tightly controlled trial to look at both alternative therapies, there was no benefit to their use for pain or stiffness.
All 45 patients tested a copper bracelet, two different magnetic wrist straps, and a demagnetised version.
An arthritis charity said people should not waste their money on the therapies.
Study leader Stewart Richmond, a research fellow in the Department of Health Sciences, said there had only been one other randomised controlled trial - comparing the treatment with placebo - on copper bracelets and that was done in the 1970s.
The market - particularly in magnetic devices which can cost £25 and £65 for the wrist straps - is worth billions of dollars worldwide.
In the trial, 45 people aged 50 or over, who were all diagnosed as suffering from osteoarthritis wore each of the four devices in a random order over a 16-week period.
They were all ineffective in terms of pain, stiffness and physical function, the researchers reported in the journal Complementary Therapies in Medicine.
"It appears that any perceived benefit obtained from wearing a magnetic or copper bracelet can be attributed to psychological placebo effects," said Mr Richmond.
"People tend to buy them when they are in a lot of pain, then when the pain eases off over time they attribute this to the device.
"However, our findings suggest that such devices have no real advantage over placebo wrist straps that are not magnetic and do not contain copper."