Rangers avoided relegation by finishing 10th but the club was later charged for failing to implement Haveron's touchline ban against Dungannnon.
It could have resulted in Carrick losing three points and being relegated but the Irish FA decided not to apply any sanction following a hearing.
Haveron replaced Michael Hughes as Rangers boss in September 2013.
"The Board of Carrick Rangers FC can announce that we have accepted the resignation of manager Gary Haveron and assistant manager Steven Mills," said the club on Monday.
"Following discussions between the Board and the management team, we were unable to establish a mutual agreement on the best way forward for the club."
He guided Carrick to Championship success in his first full season and with it a return to top-flight football.
Last month's dramatic 2-1 victory over Ballinamallard United on the final day of the season moved Carrick from the bottom to 10th and safety.
Their Premiership status was threatened by the touchline charge but the IFA Disciplinary opted to "exercise its discretion" in not imposing a sanction.
Warrenpoint Town, who finished bottom but just a point behind Carrick, have appealed the IFA ruling.
Gary Haveron has resigned as manager of Premiership side Carrick Rangers after a controversial end to the season.