With ∼60 % of global energy lost as heat, technologies such as thermoelectric generators (TEGs) are an important route to enhancing the efficiency of energy-intensive processes. Optimising thermoelectric (TE) materials requires balancing a set of interdependent physical properties to meet efficiency, cost and sustainability requirements, and is a complex materials-design challenge. In this study, we demonstrate a fully first-principles modelling approach to calculating the properties and thermoelectric figure of merit ZT and apply it to the orthorhombic and rhombohedral phases of GeS and GeSe. We predict a large ZTmax = 2.12 for n-doped Pnma GeSe at 900 K, which would make it a good match for p-type SnSe in a thermoelectric couple. In contrast to the more usual p-type doping, the electrical conductivity σ is largest along the layering direction, which would combine with the low κlatt to produce a much larger ZTmax > 3 if the growth direction could be controlled. We also predict that p-doped R3m GeS and GeSe can achieve an industrially-viable ZT > 1, through a high σ counterbalanced by a large thermal conductivity, and experiments indicate this can be further improved by alloying. Our results therefore strongly motivate further study of the under-explored Ge chalcogenides as prospective TEs, with particular focus on strategies for n-doping the Pnma phases.