We present a variational pseudo self-interaction correction density functional approach (VPSIC) to the ab initio theoretical description of correlated solids and molecules. The approach generalizes previous nonvariational versions based on plane waves (pseudo self-interaction correction) or atomic orbital (atomic self-interaction correction). The VPSIC approach provides well-defined total energies and forces and enables structural optimization and dynamics, aside from providing high-quality electronic-structure-related properties as the previous methods. A variety of demanding test cases, including nonmagnetic and magnetic correlated oxides (e. g., manganites and d(1) titanates) and a large database of molecules, indicate a high accuracy of the method in predicting structural and electronic properties. This represents a considerable improvement over standard local density functionals at a similar computational cost.