Geomagnetically induced currents (GICs) cause half cycle saturation of transformers, which increases harmonic currents and reactive powers in the grid. This paper presents the least-squares (LS) estimation of the geoelectric field using the GIC measurements for model validation purposes. To account for more realistic noise scenarios, a general probabilistic GIC measurement model has been developed. Using the proposed model, the accuracy of the LS estimator and its reliability in assessing the geoelectric field are available analytically. The analytical results are verified through numerical simulations using a practical 20-bus test case.