Vale currently sit second-bottom in the table, having managed to collect just five points from eight games.
That has prompted Adams to leave Vale Park with immediate effect.
He 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.
"I believe now is the time for another manager to take the helm and I would like to thank [Vale chairman] Norman Smurthwaite and his wife Lorraine for their fantastic support. I wish the club every success for this season and the future."
Adams first moved to Vale Park in 2009 before leaving the following year with the club top of League Two to join boyhood club Sheffield United.
After an unsuccessful spell at Bramall Lane, he returned to Vale - who did not secure promotion in the year of his departure - and has since steered the club through choppy financial waters.
Adams took the club back to League One in 2012-13 and enjoyed a fine campaign last time out when steering his side to a ninth-placed finish.