The evolved solar-type stars 16 Cyg A and B have long been studied as solar analogs, yielding a glimpse into the future of our own Sun. The orbital period of the binary system is too long to provide meaningful dynamical constraints on the stellar properties, but asteroseismology can help because the stars are among the brightest in the Kepler field. We present an analysis of three months of nearly uninterrupted photometry of 16 Cyg A and B from the Kepler space telescope. We extract a total of 46 and 41 oscillation frequencies for the two components, respectively, including a clear detection of octupole (l = 3) modes in both stars. We derive the properties of each star independently using the Asteroseismic Modeling Portal, fitting the individual oscillation frequencies and other observational constraints simultaneously. We evaluate the systematic uncertainties from an ensemble of results generated by a variety of stellar evolution codes and fitting methods. The optimal models derived by fitting each component individually yield a common age (t = 6.8 +/- 0.4 Gyr) and initial composition (Z(i) = 0.024 +/- 0.002, Y-i = 0.25 +/- 0.01) within the uncertainties, as expected for the components of a binary system, bolstering our confidence in the reliability of asteroseismic techniques. The longer data sets that will ultimately become available will allow future studies of differential rotation, convection zone depths, and long-term changes due to stellar activity cycles.