Analyses of spectra obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite, together with spectra from the Copernicus and interstellar medium absorption profile spectrograph (IMAPS) instruments, reveal an unexplained, very wide range in the observed deuterium/hydrogen (D/H) ratios for interstellar gas in the Galactic disk beyond the Local Bubble. We argue that spatial variations in the depletion of deuterium onto dust grains can explain these local variations in the observed gas-phase D/H ratios. We present a variable deuterium depletion model that naturally explains the constant measured values of D/H inside the Local Bubble, the wide range of gas-phase D/H ratios observed in the intermediate regime [logN(HI)=19.2-20.7], and the low gas-phase D/H ratios observed at larger hydrogen column densities. We consider empirical tests of the deuterium depletion hypothesis: (1) correlations of gas-phase D/H ratios with depletions of the refractory metals iron and silicon, and (2) correlation with the H2 rotational temperature. Both of these tests are consistent with deuterium depletion from the gas phase in cold, not recently shocked regions of the ISM, and high gas-phase D/H ratios in gas that has been shocked or otherwise heated recently. We argue that the most representative value for the total (gas plus dust) D/H ratio within 1 kpc of the Sun is >=23.1+/-2.4(1σ) parts per million (ppm). This ratio constrains Galactic chemical evolution models to have a very small deuterium astration factor, the ratio of primordial to total (D/H) ratio in the local region of the Galactic disk, which we estimate to be fd<=1.19+0.16-0.15(1σ) or <=1.12+/-0.14(1σ) depending on the adopted light-element nuclear reaction rates.Based on observations made with the NASA-CNES-CSA Far Ultraviolet Spectroscopic Explorer. FUSE is operated for NASA by the Johns Hopkins University under NASA contract NAS5-32985.