Vale are still in administration, but all the club's other players have now put pen to paper after they re-issued contracts to existing players who agreed deals at the end of last season, along with new players who signed in the summer.
Although Artell originally agreed a two-year deal with the League Two side, the 31-year-old defender has now opted not to sign.
Manager Micky Adams told the club's official website: "I'm very disappointed, both personally and professionally, as I genuinely believed that Dave would stick with the club.
"These have been uncertain times for the club and I believe Dave has attracted interest from other clubs. However, we have worked with him for the whole of the pre-season period and I am very disappointed to see him leave."
Adams added: "I am relieved that the majority of players have committed their futures to Port Vale at such a difficult time, although I'm also disappointed that this situation has presented an opportunity for one of our players to leave the club. It is very important that we unite as a club moving forward and I look forward to seeing our fans at Vale Park."
