The winger, 27, was one of 10 players offered fresh terms by the newly-promoted League One club at the start of May but Vincent has snubbed the two-year deal on the table in favour of looking elsewhere for another club.
Manager Micky Adams told Vale's official website: "I am personally disappointed that we couldn't reach an agreement with Ashley but that is football and we move on.
"I'd like to thank Ashley for his contribution for his time at Port Vale, particularly in the first half of the season."
Vincent joined the Valiants from Colchester last summer and made 40 appearances this season, scoring eight goals.
- Sports & Recreation