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We derive improved system parameters for the HD 209458 system using a model that simultaneously fits both photometric transit and radial velocity observations. The photometry consists of previous Hubble Space Telescope STIS and FGS observations, 12 I-band transits observed between 2001 and 2003 with the Mount Laguna Observatory 1 m telescope, and six Strömgren b + y transits observed between 2001 and 2004 with two of the Automatic Photometric Telescopes at Fairborn Observatory. The radial velocities were derived from Keck HIRES observations. The model properly treats the orbital dynamics of the system and thus yields robust and physically self-consistent solutions. Our set of system parameters agrees with previously published results, although with improved accuracy. For example, applying robust limits on the stellar mass of 0.93-1.20 M☉, we find 1.26RJ < Rplanet < 1.42RJ and 0.59MJ < Mplanet < 0.70MJ. We can reduce the uncertainty of these estimates by including a stellar mass-radius relation constraint, yielding Rplanet = RJ and Mplanet = MJ. Our results verify that the planetary radius is 10%-20% larger than predicted by irradiated planet evolution models, confirming the need for an additional mechanism to slow the evolutionary contraction of the planet. A revised ephemeris is derived, T0 = 2,452,854.82545 + 3.52474554E (HJD), which now contains an uncertainty in the period of 0.016 s and should facilitate future searches for planetary satellites and other bodies in the HD 209458 system.