Time- and angle-resolved two-photon-photoelectron (2PPE) spectroscopy is used to investigate the femtosecond dynamics of electron localization and solvation in ultrathin ice layers adsorbed on a Cu(111) single-crystal surface. An ultrashort UV pump pulse excites electrons in the Cu substrate to electronic states above the Fermi level (E-F), whereby wave function overlap with the conduction band of the ice mediates electron transfer into the adlayer. Apart from relaxation back to the metal substrate, the conduction band electrons in the ice layer localize within the first 50 fs in an electronic state at 2.9 eV above E-F. The localization process is revealed by a pronounced temporal change in the dispersion of the binding energy with electron momentum, hk(parallel to). Subsequently, molecular reorientation stabilizes this localized electron on a picosecond time scale as observed by an increase of the binding energy with 270 meV/ps. Considering the absence of a temperature dependence in the spectra between 25 and 100 K, we exclude hopping processes of the localized electron between sites of different binding energy. We rather attribute the stabilization to electron solvation, in accordance with the line shape and the temporal evolution of the localized electronic state. By exploiting the angular dependence of the 2PPE spectra, we can separate the conduction band and the solvated, localized state in ice, which allows us to determine the position of the conduction band minimum to be 2.9 eV above E-F. While the delocalized electrons in the conduction band exhibit a positive dispersion, the characteristic feature of the solvated state is an apparently negative dispersion at all time delays. As shown by model calculations of the electron momentum distribution as a function of binding energy, this observation is consistent with a solvated, localized electron with an increasing spatial confinement of its wave function evolving in parallel to electron solvation (i.e., increasing binding energy). From the width of the k(parallel to) distribution an energy-dependent spatial extent of the probability density of the solvated electron is found which changes within 1.3 ps from about 20 Angstrom to 10 Angstrom. This finding thus corroborates the correlation of energetic stabilization and spatial extent of the electronic wave function during the process of electron solvation. On the basis of a simple model potential for a localized electron, we discuss the perturbation of the final state wave function and its influence on the analysis of angle-resolved photoemission spectra.