Earth's solid inner core grows through solidification of material from the fluid outer core onto its surface at rates of about 1mm per year, freezing in core properties over time and generating an age-depth relation for the inner core. A hemispherical structure of the inner core is well-documented: an isotropic eastern hemisphere with fast seismic velocities contrasts with a slower, anisotropic western hemisphere. Independently, the inner core is reported to super-rotate at rates of up to 1° per year. Considering the slow growth, steady rotation rates of this magnitude would erase 'frozen-in' regional variation and cannot coexist with hemispherical structure. Here, we exploit the age-depth relation, using the largest available PKIKP-PKiKP seismic travel time data set, to confirm hemispherical structure in the uppermost inner core, and to constrain the locations of the hemisphere boundaries. We find consistent eastward displacement of these boundaries with depth, from which we infer extremely slow steady inner core super-rotation of 0.1°-1° per million years. Our estimate of long-term super-rotation reconciles inner core rotation with hemispherical structure, two properties previously thought incompatible. It is in excellent agreement with geodynamo simulations, while not excluding the possibility that the much larger rotation rates inferred earlier correspond to fluctuations in inner core rotation on shorter timescales.