We report a measurement of the ratio of electric dipole transition matrix elements of cesium for the 6p(2)P(1/2) -> 7s(2)S(1/2) and 6p(2)P(3/2) -> 7s(2)S(1/2 )transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the 7s(2)S(1/2) state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of R < 7s(2)S(1/2)parallel to r parallel to 6P(2)P(3/2)>/< 7s(2)S(1/2)parallel to r parallel to 6P(2)P(1/2)> = 1.5272(17) is in excellent agreement with a theoretical prediction of R = 1.5270(27). Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of R. Combined with our recent determination of the lifetime of the 7s(2)S(1/2) state, we determine reduced matrix elements for these two transitions, < 7s(2)S(1/2)parallel to r parallel to 6P(2)P(3/2)> = -6.489(5)a(0) and < 7s(2)S(1/2)parallel to r parallel to 6P(2)P(1/2 >) = -4.249(4)a(0). These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.