It is shown that aqueous solvation free energies, Delta G(sol), can be expressed quantitatively in terms of properties of the molecular surface electrostatic potentials of the solutes. The latter are obtained computationally by the B3P86/6-31+G** density functional procedure. Regression analyses and an experimental database encompassing 50 solutes of various types are used to obtain an analytical representation of Delta G(sol) which reproduces the experimental values with a standard deviation of 1.57 kJ/mol and an average absolute deviation of 1.14 kJ/mol.