Thomas was assistant manager to Kevin Nolan at Notts County before their departure at the end of August.
He will take charge for the first time tomorrow night when Grantham travel to Matlock Town in the EVO-STIK League Premier Division.
The Gingerbreads parted company with Ian Culverhouse last week and have lost their last five league games.
A club statement said: “The club welcomes Richard and his family to the club, and we look forward to a successful time under his tenure.”
His first home game in charge will be against Halesowen Town in the FA Trophy first qualifying round on Saturday.
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