We report on results of a measurement of {phi} meson production in central Pb-Au collisions at E{sub lab}=158A GeV. For the first time in the history of high energy heavy-ion collisions, {phi} mesons were reconstructed both in the K{sup +}K{sup -} and the dilepton decay channels in the same experiment. This measurement yields rapidity densities near midrapidity, from the two decay channels, of 2.05{+-}0.14(stat){+-}0.25(syst) and 2.04{+-}0.49(stat){+-}0.32(syst), respectively. The shape of the measured transverse momentum spectrum is also in close agreement in both decay channels. The data rule out a possible enhancement of the {phi} yield in the leptonic over the hadronic decay channel of a factor 1.6 or larger at the 95% C.L. This rules out the discrepancy reported in the literature between measurements of the hadronic and dimuon decay channels by two different experiments.