Memristors have demonstrated immense potential as building blocks in future adaptive neuromorphic architectures. Recently, there has been focus on emulating specific synaptic functions of the mammalian nervous system by either tailoring the functional oxides or engineering the external programming hardware. However, high device-to-device variability in memristors induced by the electroforming process and complicated programming hardware are among the key challenges that hinder achieving biomimetic neuromorphic networks. Here, a simple hybrid complementary metal oxide semiconductor (CMOS)-memristor approach is reported to implement different synaptic learning rules by utilizing a CMOS-compatible memristor based on oxygen-deficient SrTiO3-x (STOx). The potential of such hybrid CMOS-memristor approach is demonstrated by successfully imitating time-dependent (pair and triplet spike-time-dependent-plasticity) and rate-dependent (Bienenstosk-Cooper-Munro) synaptic learning rules. Experimental results are benchmarked against in-vitro measurements from hippocampal and visual cortices with good agreement. The scalability of synaptic devices and their programming through a CMOS drive circuitry elaborates the potential of such an approach in realizing adaptive neuromorphic computation and networks.