This paper presents a new method to design a current controller for grid-tied inverters under both balanced and unbalanced grid voltage conditions. The proposed controller consists of combining a feedback-output controller with a disturbance observer (DO). The control design is carried out in the $\alpha \beta$ reference frame. Thus, the objective of the composite controller is to ensure that the output of the system tracks a sinusoidal reference signal with zero steady-state error. A feedback controller only cannot achieve a good tracking performance because of the presence of model uncertainties and unknown disturbances. To account for the natural mismatch between the actual system and the mathematical model, the system dynamics are first augmented with an additional state-variable, representing the disturbance, and the feedback controller is designed based on the assumption that the disturbance input is available for feedback. Then, an observer is constructed to estimate the disturbance, which is assumed to be a sine wave oscillating at the grid frequency. Another feature of the DO is its ability to compensate for the effect of the saturation blocks required to limit the control input during transients, leading to improved dynamic performance. Several experimental tests were conducted to verify the effectiveness of the proposed controller, and the results demonstrated its capability to achieve accurate fast stable responses.