Dickson had been on-loan with the League Two club for the season, but has now penned a deal to 2027.
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The 21 year-old, who featured seven times for City's Under-21s in the EFL Trophy, has scored once in 15 league games for the Spireites.
Chesterfield assistant manager Gary Roberts said: "He's had a good base coming through Manchester City.
"We feel he's got good scope in him to go even better."