The 23-year-old former Manchester City reserve captain has agreed a one-year deal after a successful trial spell.
"Chesterfield is a club that's going places, it didn't need to be sold to me and it's a great step in my career," he told the club's official website.
"I'm delighted to have signed for Chesterfield and I can't wait to get going."
Brown is the club's second signing this week after former Hartlepool full-back Ritchie Humphreys arrived on Monday.
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