A correlation energy functional based on the introduction of the electron-electron coalescence cusp to the two-electron density is derived. The development of a functional based on the two-electron density, rather than the on-top density or the one-electron density, allows for an accurate assessment of the shape and width of the so-called "correlation hole" along with the errors associated with using alternatives to the two-electron density. Furthermore, such a functional completely avoids double-counting of electron correlation when applied to a two-electron density from a multireference wave function. The functional is evaluated on prototypical systems exhibiting different forms of correlation, including the helium atom, hydrogen clusters, and stretched bonds in a variety of molecules. The improvements over one-electron and on-top density functionals will be discussed along with details of the practical implementation and scaling with system size.