In this study, we investigated the nonorthogonal multiple access (NOMA) for visible light communication (VLC) Internet of Things (IoT) networks and provided a promising system design for 5G and beyond 5G applications. Specifically, we studied the capacity region of a practical uplink NOMA for multiple IoT devices with discrete and continuous inputs, respectively. For discrete inputs, we proposed an entropy approximation method to approach the channel capacity and obtain the discrete inner and outer bounds. For the continuous inputs, we derived the inner and outer bounds in closed forms. Based on these results, we further investigated the optimal receiver beamforming design for the multiple access channel (MAC) of VLC IoT networks to maximize the minimum uplink rate under receiver power constraints. By exploiting the structure of the achievable rate expressions, we showed that the optimal beamformers are the generalized eigenvectors corresponding to the largest generalized eigenvalues. Numerical results show the tightness of the proposed capacity regions and the superiority of the proposed beamformers for VLC IoT networks.