The LHCb detector has undergone a major upgrade for LHC Run 3. This Upgrade I detector facilitates operation at higher luminosity and utilises full-detector information at the LHC collision rate, critically including the use of vertex information. A new vertex locator system, the VELO Upgrade, has been constructed. The core element of the new VELO are the double-sided pixelated hybrid silicon detector modules which operate in vacuum close to the LHC beam in a high radiation environment. The construction and quality assurance tests of these modules are described in this paper. The modules incorporate 200 μm thick, n-on-p silicon sensors bump-bonded to 130 nm technology ASICs. These are attached with high precision to a silicon microchannel substrate that uses evaporative CO2 cooling. The ASICs are controlled and read out with flexible printed circuits that are glued to the substrate and wire-bonded to the chips. The mechanical support of the module is given by a carbon fibre plate, two carbon fibre rods and an aluminium plate. The sensor attachment was achieved with an average precision of 21 μm, more than 99.5% of all pixels are fully functional, and a thermal figure of merit of 3 Kcm2W-1 was achieved. The production of the modules was successfully completed in 2021, with the final assembly and installation completed in time for data taking in 2022.