The ability to fabricate materials and devices by-design at small scales, largely based in advances in lithographic and additive manufacturing methods, has led to the tremendous technological progress of the last decades. However, the growing need to structure 3D nanoscale matter for emergent functions, according to design and in a massively parallel manner, requires new means of material fabrication. Here, we demonstrate the concept and experimental realization of the encoded assembly of nanoparticles into prescribed, hierarchically ordered 3D organizations using DNA programmable bonds. Our information-constrained inverse design approach allows for encoding of targeted 3D hierarchical architectures with programmable bonds through identification of repeating mesoscale motifs and their elemental blocks, nanoscale voxels, that can also carry encoded nano-cargo. Using intrinsic symmetries of mesoscale motifs in targeted 3D architectures, we reduce the amount of information required for encoding bonds and incorporate this into the inverse design assembly strategy. As examples of this approach, we assemble spatially ordered, low-dimensional arrays with coupled plasmonic and photonic scales, a nanoscale analog of face-perovskite lattice, and a hierarchically organized lattice of spiral motifs. Detailed x-ray scattering and electron microcopy methods confirm the correspondence between the designed and realized architectures. The presented approach paves the road for establishing a by-design assembly platform for the fabrication of 3D architectures from diverse types of nanocomponents.