Wearable devices have been recently proposed to perform biometric recognition, leveraging on the uniqueness of the collectable physiological traits to generate discriminative identifiers. Most of the studies conducted on this topic have exploited heart-related signals, sensing the cardiac activity either through electrical measurements using electrocardiography, or with optical recordings employing photoplethysmography. In this paper we instead propose a system performing BIOmetric recognition using Wearable Inertial Sensors detecting Heart activity (BIOWISH). In more detail, we investigate the feasibility of exploiting mechanical measurements obtained through seismocardiography and gyrocardiography to verify the identity of a subject. Several feature extractors and classifiers, including deep learning techniques relying on siamese training, are employed to derive distinctive characteristics from the considered signals, so as to differentiate between legitimate users and impostors. A multi-session database, comprising acquisitions taken from subjects performing different activities, is employed to perform experimental tests. The obtained results testify that identifiers derived from measurements of chest vibrations, collected by wearable inertial sensors, could be employed to guarantee high recognition performance, even when considering short-time recordings. Explainability methods have been also employed to derive some insights about the aspects relevant to perform predictions for both people and activity recognition tasks.