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Wearable devices are increasingly used, thanks to the wide set of applications that can be deployed exploiting their ability to monitor physical activity and health-related parameters. Their usage has been recently proposed to perform biometric recognition, leveraging on the uniqueness of the recorded traits to generate discriminative identifiers. Most of the studies conducted on this topic have considered signals derived from cardiac activity, detecting it mainly using electrical measurements thorugh electrocardiography, or optical recordings employing photoplethysmography. In this paper we instead propose a BIOmetric recognition approach 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 recognize a person. Several feature extractors and classifiers, including deep learning techniques relying on transfer learning and siamese training, are employed to derive distinctive characteristics from the considered signals, and differentiate between legitimate and impostor subjects. An multi-session database, comprising acquisitions taken from subjects performing different activities, is employed to perform experimental tests simulating a verification system. 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.