A genuine signer's signature is naturally unstable even at short time-intervals whereas, expert forgers always try to perfectly mimic a genuine signer's signature. This presents a challenge which puts a genuine signer at risk of being denied access, while a forge signer is granted access. The implication is a high false acceptance rate (FAR) which is the percentage of forge signature classified as belonging to a genuine class. Existing work have only scratched the surface of signature verification because the misclassification error remains high. In this paper, a consensus-threshold distance-based classifier criterion is proposed for offline writer-dependent signature verification. Using features extracted from SigNet and SigNet-F deep convolutional neural network models, the proposed classifier minimizes FAR. This is demonstrated via experiments on four datasets: GPDS-300, MCYT, CEDAR and Brazilian PUC-PR datasets. On GPDS-300, the consensus threshold classifier improves the state-of-the-art performance by achieving a 1.27% FAR compared to 8.73% and 17.31% recorded in literature. This performance is consistent across other datasets and guarantees that the risk of imposters gaining access to sensitive documents or transactions is minimal.