Measuring the proper motions and geometric distances of galaxies within the Local Group is very important for our understanding of its history, present state and future. Currently, proper motion measurements using optical methods are limited only to the closest companions of the Milky Way. However, given that VLBI provides the best angular resolution in astronomy and phase-referencing techniques yield astrometric accuracies of ≈ 10 micro-arcseconds, measurements of proper motions and angular rotation rates of galaxies out to a distance of ~ 1 Mpc are feasible. This paper presents results of VLBI observations in regions of H2O maser activity of the Local Group galaxies M33 and IC 10. Two masing regions in M33 are on opposite sides of the galaxy. This allows a comparison of the angular rotation rate (as measured by the VLBI observations) with the known inclination and rotation speed of the Hi gas disk leading to a determination of a geometric distance of 730 ± 100 ± 135 kpc. The first error indicates the statistical error of the proper-motion measurements, while the second error is the systematic error of the rotation model. Within the errors, this distance is consistent with the most recent Cepheid distance to M33. Since all position measurements were made relative to an extragalactic background source, the proper motion of M33 has also been measured. This provides a three dimensional velocity vector of M33, showing that this galaxy is moving with a velocity of 190 ± 59 km s-1 relative to the Milky Way. For IC 10, we obtain a motion of 215 ± 42 km s-1 relative to the Milky Way. These measurements promise a new handle on dynamical models for the Local Group and the mass and dark matter halo of Andromeda and the Milky Way.