Adhesive type 1 pili from uropathogenic Escherichia coli strains are filamentous, supramolecular protein complexes consisting of a short tip fibrillum and a long, helical rod formed by up to several thousand copies of the major pilus subunit FimA. Here, we reconstituted the entire type 1 pilus rod assembly reaction in vitro, using all constituent protein subunits in the presence of the assembly platform FimD, and identified the so-far uncharacterized subunit FimI as an irreversible assembly terminator. We provide a complete, quantitative model of pilus rod assembly kinetics based on the measured rate constants of FimD-catalyzed subunit incorporation. The model reliably predicts the length distribution of assembled pilus rods as a function of the ratio between FimI and the main pilus subunit FimA and is fully consistent with the length distribution of membrane-anchored pili assembled in vivo. The results show that the natural length distribution of adhesive pili formed via the chaperone-usher pathway results from a stochastic chain termination reaction. In addition, we demonstrate that FimI contributes to anchoring the pilus to the outer membrane and report the crystal structures of (i) FimI in complex with the assembly chaperone FimC, (ii) the FimI-FimC complex bound to the N-terminal domain of FimD, and (iii) a ternary complex between FimI, FimA and FimC that provides structural insights on pilus assembly termination and pilus anchoring by FimI.