Ultra-high-energy (UHE) neutrinos (> 10 16 eV) can be measured cost-effectively using in-ice radio detection, which has been explored successfully in pilot arrays. A large radio detector is currently being constructed in Greenland with the potential to measure the first UHE neutrino, and an order-of-magnitude more sensitive detector is being planned with IceCube-Gen2. For such shallow radio detector stations, we present an end-to-end reconstruction of the neutrino energy and direction using deep neural networks (DNNs). The DNN determines the energy with a standard deviation of a factor of two around the true energy, which meets the science requirements of UHE neutrino detectors. For the first time, we are able to predict the neutrino direction well for all event topologies including the complicated electron neutrino charged-current (ν e -CC) interactions, a significant improvement compared to previous approaches. The obtained angular resolution follows a Gaussian distribution with σ ≈ 0.6°(0.8°) with extended tails that push the 68% quantile to 4°(5°) for non-ν e -CC and ν e -CC interactions, respectively. This highlights the advantages of DNNs for modeling the complex correlations in radio detector data, thereby enabling measurement of neutrino energy and direction.