We report on a study of exclusive radiative decays of the Upsilon(1S) resonance into the final states gamma pi^0 pi^0, gamma eta eta and gamma pi^0 eta, using 1.13 inverse femto-barn of e^+ e^- annihilation data collected at sqrt(s)= 9.46 GeV with the CLEO III detector operating at the Cornell Electron Storage Ring. In the channel gamma pi^0 pi^0, we measure the branching ratio for the decay mode Upsilon(1S) to gamma f_2(1270) to be (10.5 \pm 1.6 (+ 1.9)(-1.8)) x 10^-5. We place upper limits on the product branching ratios for the isoscalar resonances f_0(1500) and f_0(1710) for the pi^0 pi^0 and eta-eta decay channels. We also set an upper limit on the Upsilon(1S) radiative decay into pi^0 eta.