We provide a new value for the ratio R=Γ(π^{0}→e^{+}e^{-}γ(γ))/Γ(π^{0}→γγ)=11.978(6)×10^{-3}, which is by 2 orders of magnitude more precise than the current Particle Data Group average. It is obtained using the complete set of the next-to-leading-order radiative corrections in the QED sector, and incorporates up-to-date values of the π^{0}-transition-form-factor slope. The ratio R translates into the branching ratios of the two main π^{0} decay modes: B(π^{0}→γγ)=98.8131(6)% and B(π^{0}→e^{+}e^{-}γ(γ))=1.1836(6)%.