We present direct radii measurements of the well-known transiting exoplanet host stars HD 189733 and HD 209458 using the CHARA Array interferometer. We find the limb-darkened angular diameters to be thetaLD = 0.3848 +/- 0.0055 and 0.2254 +/- 0.0072 milliarcsec for HD 189733 and HD 209458, respectively. HD 189733 and HD 209458 are currently the only two transiting exoplanet systems where detection of the respective planetary companion's orbital motion from high resolution spectroscopy has revealed absolute masses for both star and planet. We use our new measurements together with the orbital information from radial velocity and photometric time series data, Hipparcos distances, and newly measured bolometric fluxes to determine the stellar effective temperatures (Teff = 4875 +/- 43, 6093 +/- 103 K), stellar linear radii (R* = 0.805 +/- 0.016, 1.203 +/- 0.061 Rsun), mean stellar densities (rho* = 1.62 +/- 0.11, 0.58 +/- 0.14 rhosun), planetary radii (Rp = 1.216 +/- 0.024, 1.451 +/- 0.074 RJup), and mean planetary densities (rhop = 0.605 +/- 0.029, 0.196 +/- 0.033 rhoJup) for HD 189733 b and HD 209458 b, respectively. The stellar parameters for HD 209458, a F9 dwarf, are consistent with indirect estimates derived from spectroscopic and evolutionary modeling. However, we find that models are unable to reproduce the observational results for the K2 dwarf, HD 189733. We show that, for stellar evolutionary models to match the observed stellar properties of HD 189733, adjustments lowering the solar-calibrated mixing length parameter from 1.83 to 1.34 need to be employed.