Self-organization of nanoparticles is an efficient strategy for producing nanostructures with complex, hierarchical architectures. The past decade has witnessed great progress in nanoparticle self-assembly, yet the quantitative prediction of the architecture of nanoparticle ensembles and of the kinetics of their formation remains a challenge. We report on the marked similarity between the self-assembly of metal nanoparticles and reaction-controlled step-growth polymerization. The nanoparticles act as multifunctional monomer units, which form reversible, noncovalent bonds at specific bond angles and organize themselves into a colloidal polymer. We show that the kinetics and statistics of step-growth polymerization enable a quantitative prediction of the architecture of linear, branched, and cyclic self-assembled nanostructures; their aggregation numbers and size distribution; and the formation of structural isomers.