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High-performance artificial synaptic devices are key building blocks for developing efficient neuromorphic computing systems. However, the nonlinear and asymmetric weight update of existing devices has restricted their practical applications. Herein, floating gate nonvolatile memory (FG NVM) devices based on two-dimensional (2D) ${\mathrm{Hf}\mathrm{S}}_{2}$/$h$-BN/FG-graphene heterostructures have been designed and investigated as multifunctional NVM and artificial optoelectronic synapses. Benefiting from the FG architecture, the ${\mathrm{Hf}\mathrm{S}}_{2}$-based NVM device exhibits competitive performances, such as a high on:off ratio ($g{10}^{5}$), large memory window (approximately 100 V), excellent charge retention ability ($g{10}^{4}\phantom{\rule{0.2em}{0ex}}\mathrm{s}$), and robust durability ($g{10}^{3}$ cycles). Notably, the artificial optoelectronic synapses based on ${\mathrm{Hf}\mathrm{S}}_{2}$ FG NVM show an impressive large conductance margin and good linearity, owing to the ultrahigh photoresponsivity and photogain of ${\mathrm{Hf}\mathrm{S}}_{2}$. The energy consumption of per spike in our artificial synapse is as low as 0.2 pJ. Therefore, a high recognition accuracy up to 91.5% of the artificial neural network on the basis of our ${\mathrm{Hf}\mathrm{S}}_{2}$-based optoelectronic synapse at the system level has been achieved, which is superior to other reported 2D artificial optoelectronic synapses. This work paves the way forward for all 2D material-based memory for developing efficient optogenetics-inspired neuromorphic computing in brain-inspired intelligent systems.