The paper is concerned with the design problem of two-degree-of-freedom (2DOF) LQI servo systems with optimal tracking characteristics for step references and optimal rejection characteristics for step disturbances. Unlike most of the literature dealing with such a problem, this paper has the following features. First, we consider such an intrinsically 2DOF design method in which the gain for the integral compensation (which takes care of the disturbance responses) can be adjusted without affecting the responses for step references. Secondly, we consider the output feedback setting, rather than the state feedback setting. To be more precise, the main contribution of this paper is to give a design method of an optimal observer for step disturbance rejection in the 2DOF context. The derivation is based on our recent analysis study that clarified the deterioration of disturbance rejection ability caused by an observer. It is also shown that the optimal observer possesses the same rejection ability as the state feedback, as long as those disturbances with certain directions are concerned.