No such luck. No major study has ever found that antioxidants make people healthier or extend life. In fact, the biggest meta-study yet done found that large doses of antioxidants seemed to shorten life. Probably that was because some of the people swallowing lots of selenium did so because they had good reason to worry, like a strong family history of cancer. But certainly nobody has found any good effects from taking these pills.
The biochemistry has been studied in detail using transgenic mice. We have gotten so good at fiddling with mouse genes that we can order up mice with just about any biochemical peculiarity. Mice have been created that overproduce the enzymes that get rid of excessive antioxidants in the body, and that therefore have fewer free radicals floating around. Their cells indeed show less evidence of being damaged by oxidants. Yet they live no longer than other mice. Nobody knows why, but a good guess, based on what we know about the body's exquisite chemical balance, is that whatever bad effects oxidants have on cells is balanced out by some good effect they have elsewhere.
Kas Thomas summarizes:
The story you've been fed about antioxidants being good for you because they stave off the buildup of toxic free radicals (which supposedly are a major cause of aging and disease)? That's all rubbish.