Micro-patterned surfaces are frequently used in high-throughput single-cell studies, as they allow one to image isolated cells in defined geometries. Commonly, cells are seeded in excess onto the entire chip, and non-adherent cells are removed from the unpatterned sectors by rinsing. Here, we report on the phenomenon of cellular self-organization, which allows for autonomous positioning of cells on micro-patterned surfaces over time. We prepared substrates with a regular lattice of protein-coated adhesion sites surrounded by PLL-g-PEG passivated areas, and studied the time course of cell ordering. After seeding, cells randomly migrate over the passivated surface until they find and permanently attach to adhesion sites. Efficient cellular self-organization was observed for three commonly used cell lines (HuH7, A549, and MDA-MB-436), with occupancy levels typically reaching 40-60% after 3-5 h. The time required for sorting was found to increase with increasing distance between adhesion sites, and is well described by the time-to-capture in a random-search model. Our approach thus paves the way for automated filling of cell arrays, enabling high-throughput single-cell analysis of cell samples without losses.