Kevin Lynch, Gerry Carr and Mark Smith have joined recently-appointed assistant manager Leam Richardson at the Proact Stadium.
Lynch has been named first-team/development coach with Carr taking over as academy director and Smith handed the role of youth-team coach.
"I'm delighted to welcome them all to the club," Cook told the club's official website.
"It was important that we had everyone in place as quickly as possible and we are all working hard now on getting ready for the new season."
Lynch resigned as manager of non-league Marine this month while Carr assisted Cook when the Spireites boss was manager of Irish side Sligo Rovers.
Smith, who started his playing career with Sheffield Wednesday, had a loan spell at Chesterfield in 1993. He was assistant manager of Notts County under Sam Allardyce and has since worked in the academies at Barnsley, Sheffield Wednesday and Sheffield United.