A disk drive includes a moveable head and a disk having a circumferential track which includes a plurality of servo wedges. The servo wedges are spaced sequentially around a circumference of the circumferential track. Each servo wedge includes an extended servo header. The disk drive includes a servo controller to perform track following with the moveable head. The servo controller compensates for servo wedge timing errors due to eccentricity associated with the servo wedges of the circumferential track by implementing: a first mode in which the servo controller locks to the extended servo header of a servo wedge and performs servo wedge timing error learning to characterize servo wedge timing errors and a second mode to adapt servo control signals of the servo controller based on the characterized servo wedge timing errors of the first mode in order to dynamically compensate for the eccentricity associated with the servo wedges.