Dobson has managed Rugby before and last season was involved in Coventry City's Academy alongside Terry Angus.
He was appointed after the departure of Rod Brown and was in charge of VS's FA Cup replay win against Midland Alliance side Friar Lane & Epworth last night.
Dobson will have a tough start to his new role as Rugby Town are currently bottom of the BGB Southern League Premier Division.
Meanwhile, former City boss Peter Reid has started work as manager of the Thailand National team.