From 1310.6×10^{6} J/ψ and 448.1×10^{6} ψ(3686) events collected with the BESIII experiment, we report the first observation of Σ^{+} and Σ[over ¯]^{-} spin polarization in e^{+}e^{-}→J/ψ[ψ(3686)]→Σ^{+}Σ[over ¯]^{-} decays. The relative phases of the form factors ΔΦ have been measured to be (-15.5±0.7±0.5)° and (21.7±4.0±0.8)° with J/ψ and ψ(3686) data, respectively. The nonzero value of ΔΦ allows for a direct and simultaneous measurement of the decay asymmetry parameters of Σ^{+}→pπ^{0}(α_{0}=-0.998±0.037±0.009) and Σ[over ¯]^{-}→p[over ¯]π^{0}(α[over ¯]_{0}=0.990±0.037±0.011), the latter value being determined for the first time. The average decay asymmetry, (α_{0}-α[over ¯]_{0})/2, is calculated to be -0.994±0.004±0.002. The CP asymmetry A_{CP,Σ}=(α_{0}+α[over ¯]_{0})/(α_{0}-α[over ¯]_{0})=-0.004±0.037±0.010 is extracted for the first time, and is found to be consistent with CP conservation.