Thin-film transistors made of solution-processed metal oxide semiconductors hold great promise for application in the emerging sector of large-area electronics. However, further advancement of the technology is hindered by limitations associated with the extrinsic electron transport properties of the often defect-prone oxides. We overcome this limitation by replacing the single-layer semiconductor channel with a low-dimensional, solution-grown In2O3/ZnO heterojunction. We find that In2O3/ZnO transistors exhibit band-like electron transport, with mobility values significantly higher than single-layer In2O3 and ZnO devices by a factor of 2 to 100. This marked improvement is shown to originate from the presence of free electrons confined on the plane of the atomically sharp heterointerface induced by the large conduction band offset between In2O3 and ZnO. Our finding underscores engineering of solution-grown metal oxide heterointerfaces as an alternative strategy to thin-film transistor development and has the potential for widespread technological applications.