Abstract The combined detection of a binary neutron-star merger in both gravitational waves (GWs) and electromagnetic (EM) radiation spanning the entire spectrum – GW170817 / AT2017gfo / GRB170817A – marks a breakthrough in the field of multi-messenger astronomy. Between the plethora of modeling and observations, the rich synergy that exists among the available data sets creates a unique opportunity to constrain the binary parameters, the equation of state of supranuclear density matter, and the physical processes at work during the kilonova and gamma-ray burst. We report, for the first time, Bayesian parameter estimation combining information from GW170817, AT2017gfo, GRB170817 to obtain truly multi-messenger constraints on the tidal deformability $\tilde{\Lambda } 𝟄 [302,860]$, total binary mass M ∈ [2.722, 2.751]M⊙, the radius of a 1.4 solar mass neutron star $R 𝟄 [11.3,13.5] \rm km$ (with additional $0.2\ \rm km$ systematic uncertainty), and an upper bound on the mass ratio of q ≤ 1.27, all at 90% confidence. Our joint novel analysis makes use of new phenomenological descriptions of the dynamical ejecta, debris disk mass, and remnant black hole properties, all derived from a large suite of numerical relativity simulations.