Former Liverpool star Money, who also enjoyed a spell with Scunthorpe as a player, managed the Iron for a year and a half between 1993 and 1994.
He went on to become head coach at Nottingham Forest whilst Frank Clark was boss at the City Ground.
Recently he has managed abroad - in Sweden with AIK Stockholm and Vasteras and in Australia for Newcastle Jets.
"He is an outstanding candidate in terms of qualifications and experience and his appointment has the unanimous approval of the board," chairman Jeff Bonser told Walsall's official site.
"We are focused on regaining our League One status at the first attempt and believe that Richard is the right man to achieve that objective."
Money has signed a two-year contract with the Saddlers, although caretaker boss Mark Kinsella will remain in charge of team affairs for Saturday's final game of the season against Barnsley.