The 32-year-old has signed a two-and-a-half year deal at Stanley to replace Paul Cook, who left the club to join Chesterfield last week.
Richardson told the club's official website: "The conversations that we've had this week have gone really well.
"I'd like to thank the chairman, Peter Marsden and Rob Heys, the board, the players, all of the staff and of course the fans for giving me this opportunity.
"This is fantastic and I'd like to think I could repay everyone with hard work and get some success at the club."
Accrington are currently in 12th place in the League Two table.