Unmanned aerial vehicles (UAVs) are foreseen to constitute promising airborne communication devices as a benefit of their superior channel quality. But UAV-to-ground (U2G) communications are vulnerable to eavesdropping. Hence, we conceive a sophisticated physical layer security solution for improving the secrecy rate of multi-antenna aided U2G systems. Explicitly, the secrecy rate of the U2G MIMO wiretap channels is derived by using random matrix theory. The resultant explicit expression is then applied in the joint optimization of the MIMO transceiver and the UAV location relying on an alternating optimization technique. Our numerical results show that the joint transceiver and location optimization conceived facilitates secure communications even in the challenging scenario, where the legitimate channel of confidential information is inferior to the eavesdropping channel.