Urban space is highly heterogeneous, with economic and population activities concentrating in localized centers. However, the global organization of such intra-urban centers remains poorly understood due to the lack of consistent, comparable data. Here we develop a scalable geospatial framework using nighttime light observations to identify over 15,000 intra-urban centers worldwide. We uncover a robust regularity: despite differences in city size, geography, and development context, total urban area scales linearly with the number of centers, implying a roughly constant spatial footprint per center. This macroscopic regularity is underpinned by two independent sublinear scaling laws -- center number and urban area both scale with population at closely matched rates -- whose ratio cancels to produce the observed linear relationship. At the within-city level, this constancy manifests as a characteristic Voronoi coverage area per center that is consistent across regions, and centers are more regularly spaced than spatial null models predict. As a consequence, polycentric cities maintain stable accessibility as they expand. These findings provide a new empirical foundation for understanding the spatial organization of urban growth.