It is a clear statement of intent as the Hawks aim to bounce back into National League South at the first attempt.
Relegation has hit the club hard and Bradbury, who needs to put together a competitive squad accepts that will require a different approach.
He intends to include more local talent.
Prior scored 40 goals in 57 appearances for the Rocks last season.
And Bradbury believes he fits the bill perfectly.
With the Hawks dropping into the Ryman League, Bradbury admits he is changing the focus of the team.
He said: ‘Signing Jason is a no-brainer for us as he was out of contract at Bognor.
‘He lives in Portsmouth and I am looking to build a team based on hungry local players.
‘The player is at the right age, at 27, and with lots of experience in the league we find ourselves in.
‘I have tried to get him before and he is an old-school type of centre forward.
‘He holds the ball up well, is an intelligent player and knows where the goal is.
‘As a proven goalscorer he could make all the difference to the Hawks and I am sure he will be a big success.
‘For the past two seasons we have suffered through the lack of a regular goalscorer up front.
‘Next season in the Ryman League we will need strong-willed players prepared to go the extra distance.’
Bradbury was also interested in signing Gosport Borough goalscorer Justin Bennett.
He admits, however, that the Hawks were unable to compete with what another club are offering him.
Last season’s young striker Shamir Mullings has left Westleigh Park after being released by the club.
Central-defender Ed Harris, who missed the whole of last season, has received the all-clear and has signed again for next season.
Bradbury has also agreed a deal with winger Ben Swallow to keep him at the club.