In this paper we use complex variable methods to develop the effective properties of a thermoelectric composite containing an elliptic inhomogeneity. We provide closed-form representations of the effective electric conductivity, the Seebeck coefficient, the thermal conductivity and the thermoelectric figure of merit for a square area containing the elliptic inhomogeneity. In addition, we present explicit expressions for and a discussion of the effective properties of the composite in the particular case of a circular inhomogeneity. In this case, we find that the effective figure of merit can exceed more than 6.4% of that of each constituent for a precise ratio of material parameters. Consequently, our analysis provides a new approach for improving the performance of thermoelectric devices and the design of thermoelectric composites. (C) 2019 Elsevier Ltd. All rights reserved.