The development of near-infrared (NIR) photodetection technologies is driven by emerging applications such as medical imaging or optical sensors for electronic displays and machine vision. An all-organic upconverter (OUD) is a device that converts incident NIR light directly into visible light and consists of a monolithic stack of a NIR organic photodetector (OPD) and a visible organic light-emitting diode (OLED). We present OUDs that consist of NIR heptamethine cyanine dyes/C-60 fullerene OPDs and a fluorescent tris(8-hydroxyquinolinato)aluminium (Alq(3)) OLED. The device metrics of performance are a high external quantum efficiency (EQE) of 43% of the OPD part and an OUD luminance turn-on at low bias voltages of 2 V. The dynamic response of the photocurrent and luminance is linear over a NIR light range corresponding to 26 dB. These OUDs upconvert NIR light at 830 nm to green light with a photon-to-photon conversion efficiency of 0.61%, close to the expected maximum.