The complete atomic structure of a five-monolayer film of LaAlO3 on SrTiO3 has been determined for the first time by surface x-ray diffraction in conjunction with the coherent Bragg rod analysis phase-retrieval method and further structural refinement. Cationic mixing at the interface results in dilatory distortions and the formation of metallic La(1-x)SrxTiO3. By invoking electrostatic potential minimization, the ratio of Ti{4+}/Ti{3+} across the interface was determined, from which the lattice dilation could be quantitatively explained using ionic radii considerations. The correctness of this model is supported by density functional theory calculations. Thus, the formation of a quasi-two-dimensional electron gas in this system is explained, based on structural considerations.