Excitons are composite bosons that can feature spin singlet and triplet states. In usual semiconductors, without an additional spin-flip mechanism, triplet excitons are extremely inefficient optical emitters. Transition metal dichalcogenides (TMDs), with their large spin-orbit coupling, have been of special interest for valleytronic applications for their coupling of circularly polarized light to excitons with selective valley and spin$^{1-4}$. In atomically thin MoSe$_2$/WSe$_2$ TMD van der Waals (vdW) heterostructures, the unique atomic registry of vdW layers provides a quasi-angular momentum to interlayer excitons$^{5,6}$, enabling emission from otherwise dark spin triplet excitons. Here, we report electrically tunable spin singlet and triplet exciton emission from atomically aligned TMD heterostructures. We confirm the spin configurations of the light-emitting excitons employing magnetic fields to measure effective exciton g-factors. The interlayer tunneling current across the TMD vdW heterostructure enables the electrical generation of singlet and triplet exciton emission in this atomically thin PN junction. We demonstrate electrically tunability between the singlet and triplet excitons that are generated by charge injection. Atomically thin TMD heterostructure light emitting diodes thus enables a route for optoelectronic devices that can configure spin and valley quantum states independently by controlling the atomic stacking registry.