Magnetic nanostructures with nontrivial three-dimensional (3D) shapes enable complex magnetization configurations and a wide variety of new phenomena. To date predominantly magnetic metals have been considered for nontrivial 3D nanostructures, although the magnetic and electronic transport responses are intertwined in metals. Here we report the first successful fabrication of the magnetic insulator yttrium iron garnet (Y3Fe5O12, YIG) via atomic layer deposition (ALD) and show that conformal coating of 3D objects is possible. We utilize a supercycle approach based on the combination of subnanometer thin layers of the binary systems Fe2O3 and Y2O3 in the correct atomic ratio with a subsequent annealing step for the fabrication of ALD-YIG films on Y3Al5O12 substrates. Our process is robust against typical growth-related deviations, ensuring a good reproducibility. The ALD-YIG thin films exhibit a high crystalline quality as well as magnetic properties comparable to samples obtained by other deposition techniques. We show that the ALD-YIG thin films are conformal. This enables the fabrication of 3D YIG nanostructures once appropriate nonmagnetic, 3D templates are developed. Such 3D YIG structures build the groundwork for the experimental investigation of curvature-induced changes on pure spin currents and magnon transport effects.