Vann, who has made the most of his spell at the Scholars Ground, was named on a nine-man shortlist for the gong with Walsall colleague Cockerill-Mollett also earning a place among the nominees.
The Birmingham-born centre-back, who bagged his first goal of the season as the Scholars defeated Leek Town earlier in the month, scooped the award by taking 25% of the vote.
Left-back Cockerill-Mollett finished joint second as he and recent arrival Niall Flint took 20.5% of the votes whilst George Cater and Tom Hill took 9.1% each to secure joint third place.
Chasetown confirmed that Vann will receive a trophy and beer from Bowland Brewery at their next home game, which is against Droylsden on Saturday, 5th January 2019.
