The historic detection of gravitational waves from a binary neutron star merger (GW170817) and its electromagnetic counterpart led to the first accurate (sub-arcsecond) localization of a gravitational-wave event. The transient was found to be ∼10″ from the nucleus of the S0 galaxy NGC 4993. We report here the luminosity distance to this galaxy using two independent methods. (1) Based on our MUSE/VLT measurement of the heliocentric redshift (zhelio = 0.009783 0.000023), we infer the systemic recession velocity of the NGC 4993 group of galaxies in the cosmic microwave background (CMB) frame to be vCMB = 3231 53 km s−1. Using constrained cosmological simulations we estimate the line-of-sight peculiar velocity to be vpec = 307 230 km s−1, resulting in a cosmic velocity of vcosmic = 2924 236 km s−1 (zcosmic = 0.00980 0.00079) and a distance of Dz = 40.4 3.4 Mpc assuming a local Hubble constant of H0 = 73.24 1.74 km s−1 Mpc−1. (2) Using Hubble Space Telescope measurements of the effective radius (15 5 1 5) and contained intensity and MUSE/VLT measurements of the velocity dispersion, we place NGC 4993 on the Fundamental Plane (FP) of E and S0 galaxies. Comparing to a frame of 10 clusters containing 226 galaxies, this yields a distance estimate of DFP = 44.0 7.5 Mpc. The combined redshift and FP distance is DNGC 4993 = 41.0 3.1 Mpc. This "electromagnetic" distance estimate is consistent with the independent measurement of the distance to GW170817 as obtained from the gravitational-wave signal ( D GW = 43.8 − 6.9 + 2.9 Mpc) and confirms that GW170817 occurred in NGC 4993.