Three-dimensional (3D) printing^{1,2,3,4,5,6,7,8,9} has revolutionized manufacturing processes for electronics^10,11,12, optics^13,14,15, energy^16,17, robotics¹⁸, bioengineering^19,20,21 and sensing²². Downscaling 3D printing²³ will enable applications that take advantage of the properties of micro- and nanostructures^24,25. However, existing techniques for 3D nanoprinting of metals require a polymer–metal mixture, metallic salts or rheological inks, limiting the choice of material and the purity of the resulting structures. Aerosol lithography has previously been used to assemble arrays of high-purity 3D metal nanostructures on a prepatterned substrate^26,27, but in limited geometries^{26,27,28,29,30}. Here we introduce a technique for direct 3D printing of arrays of metal nanostructures with flexible geometry and feature sizes down to hundreds of nanometres, using various materials. The printing process occurs in a dry atmosphere, without the need for polymers or inks. Instead, ions and charged aerosol particles are directed onto a dielectric mask containing an array of holes that floats over a biased silicon substrate. The ions accumulate around each hole, generating electrostatic lenses that focus the charged aerosol particles into nanoscale jets. These jets are guided by converged electric-field lines that form under the hole-containing mask, which acts similarly to the nozzle of a conventional 3D printer, enabling 3D printing of aerosol particles onto the silicon substrate. By moving the substrate during printing, we successfully print various 3D structures, including helices, overhanging nanopillars, rings and letters. In addition, to demonstrate the potential applications of our technique, we printed an array of vertical split-ring resonator structures. In combination with other 3D-printing methods, we expect our 3D-nanoprinting technique to enable substantial advances in nanofabrication.