We present time-series radial-velocity and photometric observations of a solar-type double-lined eclipsing binary star (V12) near the turnoff in the old open cluster NGC188. We use these data to determine the spectroscopic orbit and the photometric elements for V12. From our analysis we determine accurate masses (Mp=1.103+-0.007Msun, Ms=1.081+-0.007Msun) and radii (R =1.424+-0.019Rsun, Rs=1.373+-0.019Rsun) for the primary (p) and secondary (s) binary components. We adopt a reddening of E_(B-V)=0.087 for NGC188, and derive component effective temperatures of 5900+-100K and 5875+-100K, respectively, for the primary and secondary stars. From their absolute dimensions, the two components of V12 yield identical distance moduli of Vo-MV=11.24+-0.09, corresponding to 1770+-75pc. We determine an age of 6.2+-0.2Gyr for V12 and NGC188, from a comparison with theoretical isochrones in the mass-radius diagram. This age is independent of distance, reddening, and color-temperature transformations. We use isochrones from Victoria-Regina (VRSS) and Yonsei-Yale (Y2) with [Fe/H]=-0.1 and [Fe/H]=0.0. From the solar metallicity isochrones, an age of 6.4Gyr provides the best fit to the binary components for both sets of models. For the isochrones with [Fe/H]=-0.1, ages of 6.0Gyr and 5.9Gyr provide the best fits for the VRSS and Y2 models, respectively. We use the distance and age estimates for V12, together with best estimates for the metallicity and reddening of NGC188, to investigate the locations of the corresponding VRSS and Y2 isochrones relative to cluster members in the color-magnitude diagram. Plausible changes in model metallicity and distance to better match the isochrones to the cluster sequences, result in a range of ages for NGC188 that is more than 3 times that resulting from our analysis of V12.

36 pages, 10 figures (1 color), 9 tables