This paper is concerned with decentralized output regulation of hierarchical systems subject to input and output disturbances. It is assumed that the disturbance can be represented as the output of an autonomous LTI system with unknown initial state. The primary objective is to design a decentralized controller with the property that not only does it reject the degrading effect of the disturbance on the output (for a satisfactory steady-state performance), it also results in a small LQ cost function (implying a good transient behavior). To this end, the underlying problem is treated in two phases. In the first step, a number of modified systems are defined in terms of the original system. The problem of designing a LQ centralized controller which stabilizes all the modified systems and rejects the disturbance in the original system is considered, and it is shown that this centralized controller can be efficiently found by solving a LMI problem. In the second step, a method recently presented in the literature is exploited to decentralize the designed centralized controller. It is proved that the obtained controller satisfies the pre-determined design specifications including disturbance rejection. Simulation results elucidate the efficacy of the proposed control law.