Cook made the same switch when he succeeded John Sheridan at the Proact Stadium last October, leaving his then number two Richardson, 33, to step up to the top job.
As was the case then, a compensation package has been agreed between the League Two clubs.
"Having worked with him before, I'm delighted to have been able to bring in Leam," said Spireites boss Cook.
"He has great knowledge of League Two as a player, assistant manager and manager and I'm sure he's going to be a great asset to our club."
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.
After succeeding Cook, Richardson managed to keep Accrington in the Football League.
A strong end to the season saw Stanley escape relegation with a game to spare following a run of five wins in eight matches prior to a 3-0 home defeat to Oxford in their final game of the season on Saturday.
Richardson's move to the Spireites brings an end to a near eight-year association with Accrington, a club he represented 147 times as a player.