The cycloaddition of azides to alkynes is one of the most important synthetic routes to 1H-[1,2,3]-triazoles. Here a novel regiospecific copper(I)-catalyzed 1,3-dipolar cycloaddition of terminal alkynes to azides on solid-phase is reported. Primary, secondary, and tertiary alkyl azides, aryl azides, and an azido sugar were used successfully in the copper(I)-catalyzed cycloaddition producing diversely 1,4-substituted [1,2,3]-triazoles in peptide backbones or side chains. The reaction conditions were fully compatible with solid-phase peptide synthesis on polar supports. The copper(I) catalysis is mild and efficient (>95% conversion and purity in most cases) and furthermore, the X-ray structure of 2-azido-2-methylpropanoic acid has been solved, to yield structural information on the 1,3-dipoles entering the reaction. Novel Fmoc-protected amino azides derived from Fmoc-amino alcohols were prepared by the Mitsunobu reaction.