The engineering of biological molecules is a key concept in the design of highly functional, sophisticated soft materials. Biomolecules exhibit a wide range of functions and structures, including chemical recognition (of enzyme substrates or adhesive ligands1, for instance), exquisite nanostructures (composed of peptides2, proteins3 or nucleic acids4), and unusual mechanical properties (such as silk-like strength3, stiffness5, viscoelasticity6 and resiliency7). Here we combine the computational design of physical (noncovalent) interactions with pathway-dependent, hierarchical 'click' covalent assembly to produce hybrid synthetic peptide-based polymers. The nanometre-scale monomeric units of these polymers are homotetrameric, α-helical bundles of low-molecular-weight peptides. These bundled monomers, or 'bundlemers', can be designed to provide complete control of the stability, size and spatial display of chemical functionalities. The protein-like structure of the bundle allows precise positioning of covalent linkages between the ends of distinct bundlemers, resulting in polymers with interesting and controllable physical characteristics, such as rigid rods, semiflexible or kinked chains, and thermally responsive hydrogel networks. Chain stiffness can be controlled by varying only the linkage. Furthermore, by controlling the amino acid sequence along the bundlemer periphery, we use specific amino acid side chains, including non-natural 'click' chemistry functionalities, to conjugate moieties into a desired pattern, enabling the creation of a wide variety of hybrid nanomaterials.