We use density-functional theory plus dynamical mean-field theory to demonstrate the emergence of a metallic layer at the interface between the two Mott insulators LaTiO3 and LaVO3. The metallic layer is due to charge transfer across the interface, which alters the valence state of the transition-metal cations close to the interface. Somewhat counterintuitively, the charge is transferred from the Ti cations with formal d1 electron configuration to the the V cations with formal d2 configuration, thereby increasing the occupation difference of the t2g states. This can be understood as a result of a gradual transition of the charge-transfer energy, or electronegativity, across the interface. The spatial extension of the metallic layer, in particular toward the LaTiO3 side, can be controlled by epitaxial strain, with tensile strain leading to a localization within a thickness of only two unit cells. Our results open up a route for creating a tunable quasi-two-dimensional electron gas in materials with strong electronic correlations.