Upconverting semiconductor quantum dots (QDs) combine the stability of an inorganic crystalline structure with the spectral tunability afforded by quantum confinement. Here, we present upconverting type-II/type-I colloidal double QDs that enable enhancement of the performance of near-infrared to visible photon upconversion in QDs and broadening the range of relevant materials used. The resulting ZnTe/CdSe@CdS@CdSe/ZnSe type-II/type-I double QDs possess a very high photoluminescence quantum yield, monoexponential decay dynamics, and a narrow line width, approaching those of state-of-the-art upconverting QDs. We quantitatively characterize the upconversion cross section by direct comparison with two-photon absorption when varying the pump frequency across the absorption edge. Finally, we show that these upconversion QDs maintain their optical performance in a much more demanding geometry of a dense solid film and can thus be incorporated in devices as upconversion films. Our design provides guidance for fabricating highly efficient upconverting QDs with potential applications such as security coding and bioimaging.