We present Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations of the source and lens stars for planetary microlensing event OGLE-2005-BLG-169, which confirm the relative proper motion prediction due to the planetary light curve signal observed for this event. This (and the companion Keck result) provide the first confirmation of a planetary microlensing signal, for which the deviation was only 2%. The follow-up observations determine the flux of the planetary host star in multiple passbands and remove light curve model ambiguity caused by sparse sampling of part of the light curve. This leads to a precise determination of the properties of the OGLE-2005-BLG-169Lb planetary system. Combining the constraints from the microlensing light curve with the photometry and astrometry of the HST/WFC3 data, we find star and planet masses of M_* = 0.69+- 0.02 M_solar and m_p = 14.1 +- 0.9 M_earth. The planetary microlens system is located toward the Galactic bulge at a distance of D_L = 4.1 +- 0.4 kpc, and the projected star-planet separation is a_perp = 3.5 +- 0.3 AU, corresponding to a semi-major axis of a = 4.0 (+2.2 -0.6) AU.
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