A measurement of inclusive Z to tau^+ tau^- production in pp collisions is presented, in the final states mu+hadrons, e+hadrons, e+mu, and mu+mu. The data sample corresponds to an integrated luminosity of 36 inverse picobarns collected with the CMS detector at the LHC. The measured cross section is sigma(pp to Z) B(Z to tau^+ tau^-) = 1.00 +/- 0.05 (stat.) +/- 0.08 (syst.) +/-0.04 (lumi.) nb, which is in good agreement with the next-to-next-to-leading order QCD prediction and with previous measurements in the Z to e^+e^- and mu^+ mu^- channels. The reconstruction efficiency for hadronic tau decays is determined with a precision of 7%.