We report measurements with the VLBA of the position of \sgrab with respect to two extragalactic radio sources over a period of eight years. The apparent proper motion of \sgrab relative to J1745-283 is 6.379+/-0.024 mas \peryr along a position angle of 209.60 +/- 0.18 degrees, almost entirely in the plane of the Galaxy. The effects of the orbit of the Sun around the Galactic center can account for this motion, and the residual proper motion of \sgrab perpendicular to the plane of the Galaxy is -0.4+/-0.9 km/sec . A maximum-likelihood analysis of the motion expected for a massive object within the observed Galactic center stellar cluster indicates that \sgrab contains more than about 10% of the 4 * 106 \msun deduced from stellar orbits. The intrinsic size of \sgra, as measured by several investigators, is less than 1 AU, and the implied mass density of 1022 \msun pc-3 is within about three orders of magnitude of a comparable super-massive black hole within its Schwarzschild radius. Our observations provide the first direct evidence that a compact radiative source at the center of a galaxy contains of order 106 \msun and provides overwhelming evidence that it is in the form of a super-massive black hole. Finally, the existence of ``intermediate mass'' black holes more massive than 104 \msun between roughly 103 and 105 AU from \sgrab are excluded.