As a step toward deterministic and scalable assembly of ordered spin arrays we here demonstrate a bottom-up approach to position fluorescent nanodiamonds (NDs) with nanometer precision on DNA origami structures. We have realized a reliable and broadly applicable surface modification strategy that results in DNA-functionalized and perfectly dispersed NDs that were then self-assembled in predefined geometries. With optical studies we show that the fluorescence properties of the nitrogen-vacancy color centers in NDs are preserved during surface modification and DNA assembly. As this method allows the nanoscale arrangement of fluorescent NDs together with other optically active components in complex geometries, applications based on self-assembled spin lattices or plasmon-enhanced spin sensors as well as improved fluorescent labeling for bioimaging could be envisioned.