The self-assembly of nanoparticles has attracted a vast amount of attention due to the ability of the nanostructure to control light at the sub-wavelength scale, along with consequent strong electromagnetic field enhancement. However, most approaches developed for the formation of discrete assemblies are limited to a single and homogeneous system, and incorporation of larger or asymmetrical nanoparticles into assemblies with high purity remains a key challenge. Here, a simple and versatile approach to assemble nanoparticles of different sizes, shapes, and materials into various discrete homo- or hetero-structures using only two complementary deoxyribonucleic acid (DNA) strands is presented. First, surface functionalisation using DNA and alkyl-polyethylene glycol (PEG) enables transformation of as-synthesised nanoparticles into readily usable plasmonic building blocks for self-assembly. Optimisation of the DNA coverage enables the production of different assembly types, such as homo- and hetero-dimers, trimers and tetramers and core-satellite structures, which are produced in high purity using electrophoresis purification. The approach is extended from purely plasmonic structures to incorporate (luminescent) semiconductor nanoparticles for formation of hybrid assemblies. The deposited assemblies form a high yield of specific geometrical arrangements, attributed to the van der Waals attraction between particles. This method will enable the development of new complex colloidal nanoassemblies for biological and optical applications.