The League One outfit have confirmed that the 52-year-old "reluctantly" made the decision to resign following lengthy talks with chairman Norman Smurthwaite.
Adams, who guided the club to League One promotion, spent one season at Vale Park in 2009, but returned in 2011 following a brief stint at Sheffield United.
Adams told the club's official website: "It is with great sadness that I have decided to leave Port Vale but I believe I am leaving the club in a stronger position than when I joined.
"I have spent five years in Burslem, punctuated by a spell at Sheffield United, and although the role of a football manager brings with it a roller-coaster of emotions, I will never forget my time at Vale and the many happy memories I will take away with me.
"This has not been an easy decision to make, which has been made even more difficult by the strong relationships I have forged during my time at the club. I would like to thank my immediate team, all of the staff at Vale Park and the many players I have worked with throughout my two spells. I have met some truly fantastic people.
"In addition, I would like to thank all of the Port Vale fans for their fantastic support. I hope that the club has only bright times ahead."
Smurthwaite added: "Throughout the time I have known him, he has led the club with great passion and professionalism and it's with a heavy heart that I accept his resignation today."
Port Vale are currently second from bottom in the league table after picking up five points from eight matches.