The self-assembly of nanoscale elements into three-dimensional structures with precise shapes and sizes is important in fields such as nanophotonics, metamaterials and biotechnology. Short molecular linkers have previously been used to create assemblies of nanoparticles, but the approach is limited to small interparticle distances, typically less than 10 nm. Alternatively, DNA origami can precisely organize nanoscale objects over much larger length scales. Here we show that rigid DNA origami scaffolds can be used to assemble metal nanoparticles, quantum dots and organic dyes into hierarchical nanoclusters that have a planet-satellite-type structure. The nanoclusters have a tunable stoichiometry, defined distances of 5-200 nm between components, and controllable overall sizes of up to 500 nm. We also show that the nanoscale components can be positioned along the radial DNA spacers of the nanostructures, which allows short- and long-range interactions between nanoparticles and dyes to be studied in solution. The approach could, in the future, be used to construct efficient energy funnels, complex plasmonic architectures, and porous, nanoengineered scaffolds for catalysis.