A wide variety of new phenomena such as novel magnetization configurations have been predicted to occur in three dimensional magnetic nanostructures. However, the fabrication of such structures is often challenging due to the specific shapes required, such as magnetic tubes and spirals. Furthermore, the materials currently used to assemble these structures are predominantly magnetic metals that do not allow to study the magnetic response of the system separately from the electronic one. In the field of spintronics, the prototypical material used for such experiments is the ferrimagnetic insulator yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$, YIG). YIG is one of the best materials especially for magnonic studies due to its low Gilbert damping. Here, we report the first successful fabrication of YIG thin films via atomic layer deposition. To that end we utilize a supercycle approach based on the combination of sub-nanometer thin layers of the binary systems Fe$_2$O$_3$ and Y$_2$O$_3$ in the correct atomic ratio on Y$_3$Al$_5$O$_{12}$ substrates with a subsequent annealing step. Our process is robust against typical growth-related deviations, ensuring a good reproducibility. The ALD-YIG thin films exhibit a good crystalline quality as well as magnetic properties comparable to other deposition techniques. One of the outstanding characteristics of atomic layer deposition is its ability to conformally coat arbitrarily-shaped substrates. ALD hence is the ideal deposition technique to grant an extensive freedom in choosing the shape of the magnetic system. The atomic layer deposition of YIG enables the fabrication of novel three dimensional magnetic nanostructures, which in turn can be utilized for experimentally investigating the phenomena predicted in those structures.