Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the target’s surface. Reconstructing the conductivity distribution is known to be an ill-posed inverse problem whose solutions are highly intolerant to modeling errors. To achieve sufficient accuracy, very dense meshes are usually needed in a finite element approximation of the EIT forward model. This leads to very high-dimensional problems and often unacceptably tedious computations for real-time applications. We consider the model reduction in EIT within the Bayesian inversion framework. We construct the reduced-order model by proper orthogonal decompositions (POD) of the electrical conductivity and the potential distributions. The associated POD modes are computed based on a priori information on the conductivity. The feasibility of the reduced-order model is tested both numerically and with experimental data. The proposed approach is shown to speed up EIT reconstruction considerably without significantly decreasing image quality. In the selected test cases, high-quality reconstructions are obtained with the reduced-order model in 3.5% to 5% of the time required for conventional reconstructions.