The Lancashire official has previously taken charge of one game involving the Magpies - a 4-0 home win over Rotherham United in January 2017.
So far this term, he's been the man in the middle on five occasions (four Championship games and one in the Carabao Cup). He's shown 15 yellow cards and one red.
Last season he refereed 42 matches in all competitions, showing 167 yellow cards and flashing ten reds.
Kick-off at the City Ground is at 7.45pm (BST) on Wednesday and Simpson will be assisted by Michael George and Nigel Lugg.
The fourth official will be Michael Salisbury.