Resistive switching (RS) devices with binary and analogue operation are expected to play a key role in the hardware implementation of artificial neural networks. However, state of the art RS devices based on binary oxides (e.g., HfO2) still do not exhibit enough competitive performance. In particular, variability and yield still need to be improved to fit industrial requirements. In this study, we fabricate RS devices based on a TaOx/HfO2 bilayer stack, using a novel methodology that consists of the in situ oxidation of a Ta film inside the atomic layer deposition (ALD) chamber in which the HfO2 film is deposited. By means of X-ray reflectivity (XRR) and time-of-flight secondary ion mass spectrometry (ToF-SIMS), we realized that the TaOx film shows a substoichiometric structure, and that the TaOx/HfO2 bilayer stack holds a well-layered structure. An exhaustive electrical characterization of the TaOx/HfO2-based RS devices shows improved switching performance compared to the single-layer HfO2 counterparts. The main advantages are higher forming yield, self-compliant switching, lower switching variability, enhanced reliability, and better synaptic plasticity.