Chilvers made 21 appearances for Micky Adams' men last season following his arrival on loan from AFC Telford and the experienced centre-half scored two vital late goals against Rochdale and Northampton towards the end of the campaign to help Vale secure promotion to League One.
The 31-year-old told the club's official website: "It has been good to eventually get it signed.
"I've been away on holiday and people have been away at the club, it's just been a case of getting us both together at the same time to do it. I'm delighted."
Following the departures of Darren Purse and John McCombe, Chilvers is now the most experienced central defender at Vale Park - with young Joe Davis the only other recognised centre-back.
The former Arsenal trainee added: "At the end of the season when I spoke to Micky he said he'd be bringing in other centre-backs and it would just be down to if you do well enough in pre-season to be playing.
"I've been keeping an eye out to see just in general who we've been signing, I will just have to wait and see what happens."
- Sports & Recreation
- Micky Adams
- AFC Telford