Cities grow in a bottom-up manner, leading to fractal-like urban morphology characterized by scaling laws. Correlated percolation has succeeded in modeling urban geometries by imposing strong spatial correlations. However, the origin of such correlations remains largely unknown. Very recently, our understanding of human movements has been revolutionized thanks to the increasing availability of large-scale human mobility data. This paper proposes a novel human movement model that offers a micro-foundation for the dynamics of urban growth. We compare the proposed model with three empirical datasets, which evidences that strong social couplings and long-memory effects are two fundamental principles responsible for the mystical spatial correlations. The model accounts for the empirically observed scaling laws, but also allows us to understand the city evolution dynamically.