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The translation of DNA sequences into corresponding biopolymers enables the production, function and evolution of the macromolecules of life. In contrast, methods to generate sequence-defined synthetic polymers with similar levels of control have remained elusive. Here, we report the development of a DNA-templated translation system that enables the enzyme-free translation of DNA templates into sequence-defined synthetic polymers that have no necessary structural relationship with nucleic acids. We demonstrate the efficiency, sequence-specificity and generality of this translation system by oligomerizing building blocks including polyethylene glycol, α-(D)-peptides, and β-peptides in a DNA-programmed manner. Sequence-defined synthetic polymers with molecular weights of 26 kDa containing 16 consecutively coupled building blocks and 90 densely functionalized β-amino acid residues were translated from DNA templates using this strategy. We integrated the DNA-templated translation system developed here into a complete cycle of translation, coding sequence replication, template regeneration and re-translation suitable for the iterated in vitro selection of functional sequence-defined synthetic polymers unrelated in structure to nucleic acids.