Richardson left Accrington, where he was manager, this week to become Cook's assistant at the Spireites.
Cook himself made the same switch in October when he succeeded John Sheridan at the Proact Stadium.
Richardson, 33, said: "It was the perfect partnership and I jumped at the chance to rejoin Paul when I knew Chesterfield were interested.
"We have the same ethos and theory on the game. My work ethic is very good, as is his. We are both opinionated, in a good way, and know the league inside out.
"I learned a lot in a short space of time with Paul and we have a very good working relationship. I'm looking forward to us working together again."
As was the case with Cook, a compensation package was agreed between the League Two clubs.
Richardson replaces Tommy Wright at Chesterfield after he left the club on Monday as part of a backroom reshuffle along with reserve-team coach Mark Crossley, development coach John Dungworth and kit man Kurt McDermott.