We present cosmological constraints from a joint analysis of the pre- and post-reconstruction galaxy power spectrum multipoles from the final data release of the Baryon Oscillation Spectroscopic Survey ( BOSS ) . Geometric constraints are obtained from the positions of BAO peaks in reconstructed spectra , which are analyzed in combination with the unreconstructed spectra in a full-shape ( FS ) likelihood using a joint covariance matrix , giving stronger parameter constraints than FS-only or BAO-only analyses . We introduce a new method for obtaining constraints from reconstructed spectra based on a correlated theoretical error , which is shown to be simple , robust , and applicable to any flavor of density-field reconstruction . Assuming \Lambda CDM with massive neutrinos , we analyze clustering data from two redshift bins z _ { \mathrm { eff } } = 0.38 , 0.61 and obtain 1.6 \% constraints on the Hubble constant H _ { 0 } , using only a single prior on the current baryon density \omega _ { b } from Big Bang Nucleosynthesis ( BBN ) and no knowledge of the power spectrum slope n _ { s } . This gives H _ { 0 } = 68.6 \pm 1.1 \mathrm { km s } ^ { -1 } \mathrm { Mpc } ^ { -1 } , with the inclusion of BAO data sharpening the measurement by 40 \% , representing one of the strongest current constraints on H _ { 0 } independent of cosmic microwave background data , comparable with recent constraints using BAO data in combination with other data-sets . Restricting to the best-fit slope n _ { s } from Planck ( but without additional priors on the spectral shape ) , we obtain a 1 \% H _ { 0 } measurement of 67.8 \pm 0.7 \mathrm { km s } ^ { -1 } \mathrm { Mpc } ^ { -1 } . Finally , we find strong constraints on the cosmological parameters from a joint analysis of the FS , BAO , and Planck data . This sets new bounds on the sum of neutrino masses \sum m _ { \nu } < 0.14 \mathrm { eV } ( at 95 \% confidence ) and the effective number of relativistic degrees of freedom N _ { \mathrm { eff } } = 2.90 ^ { +0.15 } _ { -0.16 } , though contours are not appreciably narrowed by the inclusion of BAO data .