We detect high-velocity absorbing gas using Hubble Space Telescope and Far Ultraviolet Spectroscopic Explorer medium resolution spectroscopy along two high-latitude AGN sight lines (Mrk 1383 and PKS 2005-489) above and below the Galactic Center (GC). These absorptions are most straightforwardly interpreted as a wind emanating from the GC which does not escape from the Galaxy's gravitational potential. Spectra of four comparison B stars are used to identify and remove foreground velocity components from the absorption-line profiles of O VI, N V, C II, C III, C IV, Si II, Si III, and Si IV. Two high-velocity (HV) absorption components are detected along each AGN sight line, three redshifted and one blueshifted. Assuming that the four HV features trace a large-scale Galactic wind emanating from the GC, the blueshifted absorber is falling toward the GC at a velocity of 250 +/- 20 km/s, which can be explained by "Galactic fountain" material that originated in a bound Galactic wind. The other three absorbers represent outflowing material; the largest derived outflow velocity is +250 +/- 20 km/s, which is only 45% of the velocity necessary for the absorber to escape from its current position in the Galactic gravitational potential. All four HV absorbers are found to reach the same maximum height above the Galactic plane (|z_max| = 12 +/- 1 kpc), implying that they were all ejected from the GC with the same initial velocity. The derived metallicity limits of >10-20% Solar are lower than expected for material recently ejected from the GC unless these absorbers also contain significant amounts of hotter gas in unseen ionization stages.