Reconstituting tissues from their cellular building blocks facilitates the modeling of morphogenesis, homeostasis and disease in vitro. Here we describe DNA-programmed assembly of cells (DPAC), a method to reconstitute the multicellular organization of organoid-like tissues having programmed size, shape, composition and spatial heterogeneity. DPAC uses dissociated cells that are chemically functionalized with degradable oligonucleotide 'Velcro', allowing rapid, specific and reversible cell adhesion to other surfaces coated with complementary DNA sequences. DNA-patterned substrates function as removable and adhesive templates, and layer-by-layer DNA-programmed assembly builds arrays of tissues into the third dimension above the template. DNase releases completed arrays of organoid-like microtissues from the template concomitant with full embedding in a variety of extracellular matrix (ECM) gels. DPAC positions subpopulations of cells with single-cell spatial resolution and generates cultures several centimeters long. We used DPAC to explore the impact of ECM composition, heterotypic cell-cell interactions and patterns of signaling heterogeneity on collective cell behaviors.