We study optomechanically induced amplification and perfect transparency in a double-cavity optomechanical system. We find that if two control lasers with appropriate amplitudes and detunings are applied to drive the system, optomechanically induced amplification of a probe laser can occur. In addition, perfect optomechanically induced transparency, which is robust to mechanical dissipation, can be realized by the same type of driving. These results indicate important progress toward signal amplification, light storage, fast light, and slow light in quantum information processes.