© 2015. The American Astronomical Society. All rights reserved. We present a model for the evolution of the galaxy ultraviolet (UV) luminosity function (LF) across cosmic time where star formation is linked to the assembly of dark matter halos under the assumption of a mass-dependent, but redshift-independent, efficiency. We introduce a new self-consistent treatment of the halo star formation history, which allows us to make predictions at z > 10 (lookback time ≲500 Myr), when growth is rapid. With a calibration at a single redshift to set the stellar-to-halo mass ratio, and no further degrees of freedom, our model captures the evolution of the UV LF over all available observations (0 ≲ z ≲ 10). The significant drop in luminosity density of currently detectable galaxies beyond z ∼ 8 is explained by a shift of star formation toward less massive, fainter galaxies. Assuming that star formation proceeds down to atomic cooling halos, we derive a reionization optical depth T = 0.056+0.007-0.010, fully consistent with the latest Planck measurement, implying that the universe is fully reionized at z = 7.84+0.65-0.98. In addition, our model naturally produces smoothly rising star formation histories for galaxies with L ≲ L∗ in agreement with observations and hydrodynamical simulations. Before the epoch of reionization at z > 10 we predict the LF to remain well-described by a Schechter function, but with an increasingly steep faint-end slope (α ∼ -3.5 at z ∼ 16). Finally, we construct forecasts for surveys with James Webb Space Telescope (JWST) and Wide-field Infrared Survey Telescope (WFIRST) and predict that galaxies out to z ∼ 14 will be observed. Galaxies at z > 15 will likely be accessible to JWST and WFIRST only through the assistance of strong lensing magnification.