We present the numerically integrated orbits of Pluto’s satellites. The orbits have been fit to a data set that includes Earth-based and Hubble Space Telescope (HST) astrometry of Charon, Nix, Hydra, Kerberos, and Styx, as well as the lightcurves from the Pluto–Charon mutual events. We also report new, 2010–2012 HST astrometry of all satellites including recently discovered Styx plus a pre-discovery detection of Kerberos in 2006. Pluto-relative data sets have been corrected for the center-of-light vs. center-of-mass offsets with the Pluto albedo model. The results are summarized in terms of the postfit residuals, state vectors, and mean orbital elements. Orbits of Charon, Styx, Nix, and Kerberos are nearly circular, while Hydra’s shows a small eccentricity. All satellites are in near-resonance conditions, but we did not uncover any resonant arguments. Our model yields 975.5±1.5km3s−2, 869.6±1.8km3s−2, and 105.9±1.0km3s−2 for the system’s, Pluto’s, and Charon’s GM values. The uncertainties reflect both systematic and random measurement errors. The GM values imply a bulk density of 1.89±0.06gcm−3 for Pluto and 1.72±0.02gcm−3 for Charon. We also obtain GMNix=0.0030±0.0027km3s−2 GMHydra=0.0032±0.0028km3s−2, GMKerberos=0.0011±0.0006km3s−2, and an upper bound on Styx’s GM of 0.0010km3s−2. The 1σ errors are based on the formal covariance from the fit and they reflect only measurement errors. In-orbit (or along the track), radial, and out-of-plane orbital uncertainties at the time of New Horizons encounter are on the order of few tens of km or less for Charon, Nix, and Hydra. Kerberos and Styx have their largest uncertainty component of ∼140km and ∼500km respectively in the in-orbit direction.