The 26-year-old has been rewarded for some impressive displays during the Addicks' title-winning season having joined non-league Hayes & Yeading last summer following a successful trial spell.
"I'm really pleased Bradley has agreed to extend his contract," manager Chris Powell told the club website.
"He was - and he knows it - a bit of a punt, shall we say. But he showed enough to me in the season before last, in the weeks that he was here on trial, that he was worthy of having a season at professional level.
"He made the breakthrough quicker than anyone could have expected. We saw the attributes in him and felt even at his late age that he was worth giving a chance to."