He replaces ex-Bury chief Andy Preece, who quit Vics last month to become director of football at Welsh Premier League outfit Airbus UK.
Simpson will be assisted by one-time Blackburn and Aston Villa defender Alan Wright.
The new pair will take charge for the first time when Northwich, who were evicted from their Victoria Stadium ground a fortnight ago, face Hampton and Richmond Borough in the FA Trophy third round tie at Macclesfield Town on Saturday.
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