Solution-processed electronic and optoelectronic^,,, devices offer low cost, large device area, physical flexibility and convenient materials integration compared to conventional epitaxially grown, lattice-matched, crystalline semiconductor devices. Although the electronic or optoelectronic performance of these solution-processed devices is typically inferior to that of those fabricated by conventional routes, this can be tolerated for some applications in view of the other benefits. Here we report the fabrication of solution-processed infrared photodetectors that are superior in their normalized detectivity (D*, the figure of merit for detector sensitivity) to the best epitaxially grown devices operating at room temperature. We produced the devices in a single solution-processing step, overcoating a prefabricated planar electrode array with an unpatterned layer of PbS colloidal quantum dot nanocrystals. The devices showed large photoconductive gains with responsivities greater than 10³ A W^-1. The best devices exhibited a normalized detectivity D* of 1.8 × 10¹³ jones (1 jones = 1 cm Hz^1/2 W^-1) at 1.3 µm at room temperature: today's highest performance infrared photodetectors are photovoltaic devices made from epitaxially grown InGaAs that exhibit peak D* in the 10¹² jones range at room temperature, whereas the previous record for D* from a photoconductive detector lies at 10¹¹ jones. The tailored selection of absorption onset energy through the quantum size effect, combined with deliberate engineering of the sequence of nanoparticle fusing and surface trap functionalization, underlie the superior performance achieved in this readily fabricated family of devices.