It has been well established that both in bulk at ambient pressure and for films under modest strains, cubic SrCoO3−δ (δ<0.2) is a ferromagnetic metal. Recent theoretical work, however, indicates that a magnetic phase transition to an antiferromagnetic structure could occur under large strain accompanied by a metal-insulator transition. We have observed a strain-induced ferromagnetic-to-antiferromagnetic phase transition in SrCoO3−δ films grown on DyScO3 substrates, which provide a large tensile epitaxial strain, as compared to ferromagnetic films under lower tensile strain on SrTiO3 substrates. Magnetometry results demonstrate the existence of antiferromagnetic spin correlations and neutron diffraction experiments provide a direct evidence for a G-type antiferromagnetic structure with Neél temperatures between TN∼135±10K and ∼325±10K, depending on the oxygen content of the samples. Therefore, our data experimentally confirm the predicted strain-induced magnetic phase transition to an antiferromagnetic state for SrCoO3−δ thin films under large epitaxial strain.