The Cu-catalyzed azide-alkyne cycloaddition (CuAAC) reaction is a cornerstone method for the ligation of biomolecules. However, undesired Cu-mediated oxidation and Cu-contamination in bioconjugates limits biomedical utility. Here, we report a generic CuAAC flow platform for the rapid, robust, and broad-spectrum formation of discrete triazole bioconjugates. This process leverages an engineering problem to chemical advantage: solvent-mediated Cu pipe erosion generates ppm levels of Cu in situ under laminar flow conditions. This is sufficient to catalyze the CuAAC reaction of small molecule alkynes and azides, fluorophores, marketed drug molecules, peptides, DNA, and therapeutic oligonucleotides. This flow approach, not replicated in batch, operates at ambient temperature and pressure, requires short residence times, avoids oxidation of sensitive functional groups, and produces products with very low ppm Cu contamination.