Handwritten signatures are used in authentication systems as a universal biometric identifier. Signature authenticity verification requires building and training a classifier. This paper describes a new approach to the verification of handwritten signatures by dynamic characteristics with a fuzzy rule-based classifier. It is suggested to use the metaheuristic Gravitational Search Algorithm for the selection of the relevant features and tuning fuzzy rule parameters. The efficiency of the approach was tested with an original dataset; the type II errors in finding the signature authenticity did not exceed 0.5% for the worst model and 0.08% for the best model.