Dixon, 34, made 196 appearances throughout six seasons with the Yellows, scoring 27 goals including one in the play-off semi-final win over Matlock Town during their run to promotion last season.
Prior to his time in Warrington, he featured for the likes of Accrington Stanley, Connah's Quay Nomads, Ashton United, Marine and Salford.
In a statement explaining the reasons behind Dixon's departure, Warrington Town said: "An approach was made earlier this week by the Northern Premier League club.
"Although the club didn’t want Bohan to leave, given he is out of contract at the end of the season, we gave him permission to talk to the Silkmen.
"At the age of 34, the offer put on the table to Dixon until the end of next season to significantly increase his wage was one he felt he couldn’t turn down.
"As a result, the club has been able to negotiate a fee for his services for the remainder of this season.
"Everyone at the club wishes Bohan the very best for the future."
Photo credit: Sean Walsh Photography