Current boss John Ward becomes director of football with Rovers currently three points above Northampton Town in the second relegation place.
A double promotion winner with Salisbury, Clarke left the Conference club last summer to become Ward's number two and now takes charge with immediate effect, starting against Morecambe this weekend.
The move follows Portsmouth's decision to sack Richie Barker after just four months in charge following defeat at Rochdale in midweek.
Pompey are currently two points above the Cobblers and come to Sixfields on Easter Monday. Former player Andy Awford is in caretaker charge at Fratton Park.