Dodds, who has been at Vale Park for seven years, has put pen to paper on a one-year deal with the option of a further 12 months.
“Louis was an important player for us last season so it’s very pleasing that he has signed a new contract,” said Vale manager Rob Page.
“His versatility and creativity makes him a very valuable member of this team and I’m looking forward to working with him again next season.”
Dodds becomes the latest player to agree a new contract at Vale Park, following goalkeepers Sam Johnson and Ryan Boot, defender Nathan Smith and midfielder Ryan Lloyd.
The 28 year old made 41 appearances for the Valiants last season and scored four goals.