We present crustal velocities for 29 continuously recording GPS stations from the southern central Andes across the Puna, Eastern Cordillera, and Santa Barbara system for the period between the 27 February 2010 Maule and 1 April 2014 Iquique earthquakes in a South American frame. The velocity field exhibits a systematic decrease in magnitude from ~35 mm/yr near the trench to <1 mm/yr within the craton. We forward model loading on the Nazca-South America (NZ-SA) subduction interface using back slip on elastic dislocations to approximate a fully locked interface from 10 to 50 km depth. We generate an ensemble of models by iterating over the percentage of NZ-SA convergence accommodated at the subduction interface. Velocity residuals calculated for each model demonstrate that locking on the NZ-SA interface is insufficient to reproduce the observed velocities. We model deformation associated with a back-arc décollement using an edge dislocation, estimating model parameters from the velocity residuals for each forward model of the subduction interface ensemble using a Bayesian approach. We realize our best fit to the thrust-perpendicular velocity field with 70 ± 5% of NZ-SA convergence accommodated at the subduction interface and a slip rate of 9.1 ± 0.9 mm/yr on the fold-thrust belt décollement. We also estimate a locking depth of 14 ± 9 km, which places the downdip extent of the locked zone 135 ± 20 km from the thrust front. The thrust-parallel component of velocity is fit by a constant shear strain rate of -19 × 10-9 yr-1, equivalent to clockwise rigid block rotation of the back arc at a rate of 1.1°/Myr.