High precision measurements of the differential cross sections for {pi}{sup 0} photoproduction at forward angles for two nuclei, {sup 12}C and {sup 208}Pb, have been performed for incident photon energies of 4.9-5.5 GeV to extract the {pi}{sup 0}{yields}{gamma}{gamma} decay width. The experiment was done at Jefferson Lab using the Hall B photon tagger and a high-resolution multichannel calorimeter. The {pi}{sup 0}{yields}{gamma}{gamma} decay width was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value for the decay width is {Gamma}({pi}{sup 0}{yields}{gamma}{gamma})=7.82{+-}0.14(stat){+-}0.17(syst) eV. With the 2.8% total uncertainty, this result is a factor of 2.5 more precise than the current Particle Data Group average of this fundamental quantity, and it is consistent with current theoretical predictions.