Redistribution of mass in the Earth due to Pleistocene deglaciation and to present-day glacial melting induces secular changes in the Earth's gravitational field. The Earth is affected today by the former mechanism because of the viscous memory of the mantle and by the latter because of ongoing surface mass redistribution and related elastic response. A self-consistent procedure allows us to invert simultaneously for the lower and upper mantle viscosity and for the present-day mass imbalance in Antarctica and Greenland using the observed time variations of the long-wavelength gravity field from satellite laser ranging (SLR) analyses. The procedure is based on our normal mode relaxation theory for the forward modeling and a newly developed inversion scheme based on the Levenberg-Marquardt method. We obtain a large viscosity increase across the 670-km depth transition zone separating the upper and the lower mantle, with the lower mantle viscosity varying over the range 5 ¿ 1021 to 1022 Pa s and the less resolved upper mantle viscosity of the order of 1020 Pa s. When Antarctica is the only present-day source, its rate of melting is -240 Gt yr-1, corresponding to a sea level rise of 0.7 mm yr-1; when Greenland is added as a source of ice loss, the rates of melting are -280 Gt yr-1 for Antarctica and -60 Gt yr-1 for Greenland, corresponding to sea level rises of 0.8 and 0.2 mm yr-1. SLR data indicate that ice melting in the polar regions of the Earth is ongoing.