From magnetic, specific heat, ^{170}Yb Mössbauer effect, neutron diffraction, and muon spin relaxation measurements on polycrystalline Yb_{2}Sn_{2}O_{7}, we show that below the first order transition at 0.15 K all of the Yb^{3+} ions are long-range magnetically ordered and each has a moment of 1.1μ_{B} which lies at ≃10° to a common fourfold cubic axis. The four sublattice moments have four different directions away from this axis and are therefore noncoplanar. We term this arrangement splayed ferromagnetism. This ground state has a dynamical component with a fluctuation rate in the megahertz range. The net ferromagnetic exchange interaction has an anisotropy that favors the local threefold axis. We discuss our results in terms of the phase diagram proposed by Savary and Balents [Phys. Rev. Lett. 108, 037202 (2012)] for a pyrochlore lattice of Kramers 1/2 effective spins.