The 33-year-old only took charge at the Crown Ground in November, but he has decided to accept an offer to become the assistant manager at Chesterfield.
"A formal approach has been made for the 33-year-old with a deal agreed between the two clubs after Leam indicated he wished to move on," read a statement on the club's official website.
"Leam took charge in November and led us to Football League survival last month. All at the club would like to thank him for his service as player, coach and manager over the last eight years."
Chesterfield are managed by Paul Cook, who Richardson replaced at the Accrington helm.