We present a comprehensive analysis of gamma-Z interference corrections to the weak charge of the proton measured in parity-violating electron scattering, including a survey of existing models and a critical analysis of their uncertainties. Constraints from parton distributions in the deep-inelastic region, together with new data on parity-violating electron scattering in the resonance region, result in significantly smaller uncertainties on the corrections compared to previous estimates. At the kinematics of the Qweak experiment, we determine the gamma-Z box correction to be Re\box_{gamma-Z}^V = (5.61 +- 0.36) x 10^{-3}. The new constraints also allow precise predictions to be made for parity-violating deep-inelastic asymmetries on the deuteron.