It means the former Hawks boss will be up against his old club in the National League South next season.
He left Westleigh Park before the final match of the season, following the club’s relegation.
The board at Westleigh Park replaced him with former Sutton manager Paul Doswell.
Now ex-Pompey player Bradbury has quickly got a new job with the switch to Priory Lane where he replaces Mark McGhee who had been in temporary charge and kept the team up following the departure of Jamie Howell in February.