© 2017. The American Astronomical Society. All rights reserved. Central galaxies make up the majority of the galaxy population, including the majority of the quiescent population at M∗ > 1010M⊙. Thus, the mechanism(s) responsible for quenching central galaxies play a crucial role in galaxy evolution as whole. We combine a high-resolution cosmological N-body simulation with observed evolutionary trends of the "star formation main sequence," quiescent fraction, and stellar mass function at z < 1 to construct a model that statistically tracks the star formation histories and quenching of central galaxies. Comparing this model to the distribution of central galaxy star formation rates in a group catalog of the SDSS Data Release 7, we constrain the timescales over which physical processes cease star formation in central galaxies. Over the stellar mass range 109.5-1011M⊙we infer quenching e-folding times that span 1.5-0.5 Gyr with more massive central galaxies quenching faster. For M∗ = 1010.5M⊙, this implies a total migration time of ∼4 Gyr from the star formation main sequence to quiescence. Compared to satellites, central galaxies take ∼2 Gyr longer to quench their star formation, suggesting that different mechanisms are responsible for quenching centrals versus satellites. Finally, the central galaxy quenching timescale we infer provides key constraints for proposed star formation quenching mechanisms. Our timescale is generally consistent with gas depletion timescales predicted by quenching through strangulation. However, the exact physical mechanism(s) responsible for this remain unclear.