In this paper, we present a wavefront reconstruction paradigm for NGS GLAO systems. The conventional approach to reconstructing the wavefront for LGS GLAO systems is to have a number of LGSs in a ring outside the science field and simply average the individual wavefronts. This approach is not well-suited to NGS GLAO because the stars have an irregular distribution and varying magnitudes. In this paper, we derive covariance matrices for the wavefronts in different directions and the measurement noise. Using these covariance matrices, we are able to find the minimum-variance reconstructor and estimate the residual wavefront as a function of location in the field. This can be used to determine which guide stars produce the best correction. End-to-end simulations in YAO are run to estimate the expected performance of the NGS GLAO system for the Giant Magellan Telescope. We find that there is essentially full sky coverage.