The 18-year-old joins Pools following a year at the Spireites in which he played four games in all competitions.
He was a member of Sunderland's academy from age 10 to 16, and then joined Gateshead, where he made six first-team appearances, all as a substitute.
Pools have also signed Jake's brother Lewis Orrell to the club's youth team set-up for the 2016-17 campaign.
Hartlepool United have signed striker Jake Orrell after he rejected a new deal with Chesterfield.