Lee told BBC Radio Sheffield: "I wanted to stay as I believe in what the gaffer (John Sheridan) is trying to do."
Sheridan has now tied up deals with five of the 12 players who were out of contract with the League Two champions.
Midfielder Mark Allot and strikers Dean Morgan and Drew Talbot are the other players to have signed new deals with the Spireites.
Source: BBC Sport
Source: BBC Sport