In this paper, we accurately model the transceiver hardware impairments (HWIs) of multiple-input multiple-output (MIMO) systems considering different HWI stages at transmitter and receiver. The proposed novel statistical model shows that transceiver HWIs transform the transmitted symmetric signal to asymmetric one. Moreover, it shows that the aggregate self-interference has asymmetric characteristics. Therefore, we propose improper Gaussian signaling (IGS) for transmission in order to improve the achievable rate performance. IGS is considered as a general signaling scheme which includes the proper Gaussian signaling (PGS) as a special case. Thus, IGS has additional design parameters which enable it to mitigate the HWI self-interference. As a case study, we analyze the achievable rate performance of single-input multiple-output systems with linear and selection combiner. Furthermore, we optimize the IGS statistical characteristics for interference alignment. This improves the achievable rate performance as compared to the PGS, which is validated through numerical results.