The 20-year-old has agreed a deal which will keep him at the Proact Stadium until the end of the next season.
Banks, whose father Ian was Chesterfield's assistant manager under Nicky Law, was released by Rotherham in 2012 and had been playing non-league football ever since.
Ahead of signing for FC United he turned out for North Ferriby, Scarborough Athletic and Gainsborough Trinity.
"I can't tell you how happy I am after two years out of the professional game," a delighted Banks told his new club's official website. "It's a very exciting time to be joining Chesterfield with the club at the top of the table."
Assistant boss Leam Richardson added: "He's a young lad we've identified as a very good prospect. We expect him to go on and make the first-team breakthrough and be a big part of what we're trying to do."