We present new 0.6-10 GHz observations of the binary neutron star merger GW170817 covering the period up to 300 days post-merger, taken with the Karl G. Jansky Very Large Array, the Australia Telescope Compact Array, the Giant Metrewave Radio Telescope and the MeerKAT telescope. We use these data to precisely characterize the decay phase of the late-time radio light curve. We find that the temporal decay is consistent with a power-law slope of t^-2.2, and that the transition between the power-law rise and decay is relatively sharp. Such a slope cannot be produced by a quasi-isotropic (cocoon-dominated) outflow, but is instead the classic signature of a relativistic jet. This provides strong observational evidence that GW170817 produced a successful jet, and directly demonstrates the link between binary neutron star mergers and short-hard GRBs. Using simple analytical arguments, we derive constraints on the geometry and the jet opening angle of GW170817. These results are consistent with those from our companion Very Long Baseline Interferometry (VLBI) paper, reporting superluminal motion in GW170817.