We present accurate fits for the remnant properties of generically precessing binary black holes , trained on large banks of numerical-relativity simulations . We use Gaussian process regression to interpolate the remnant mass , spin , and recoil velocity in the 7-dimensional parameter space of precessing black-hole binaries with mass ratios q \leq 2 , and spin magnitudes \chi _ { 1 } , \chi _ { 2 } \leq 0.8 . For precessing systems , our errors in estimating the remnant mass , spin magnitude , and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude ( improvement is also reported in the extrapolated region at high mass ratios and spins ) . In addition , we also model the remnant spin and kick directions . Being trained directly on precessing simulations , our fits are free from ambiguities regarding the initial frequency at which precessing quantities are defined . We also construct a model for remnant properties of aligned-spin systems with mass ratios q \leq 8 , and spin magnitudes \chi _ { 1 } , \chi _ { 2 } \leq 0.8 . As a byproduct , we also provide error estimates for all fitted quantities , which can be consistently incorporated into current and future gravitational-wave parameter-estimation analyses . Our model ( s ) are made publicly available through a fast and easy-to-use Python module called surfinBH .