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To investigate the relationship between the so-called stripe correlations and the high-T_c superconductivity, we have carried out magnetic susceptibility and zero-field muon spin relaxation measurements in partially Fe-substituted La_2−xSr_xCu_1−yFe_yO₄ (LSCFO). It has been found that the Fe substitution induces successive magnetic transitions in the overdoped regime: a spin-glass transition of Fe³⁺ spins due to the Ruderman–Kittel–Kasuya–Yosida interaction based on itinerant spins at high temperatures and a stripe-order transition of localized Cu²⁺ spins at low temperatures. The stripe-order transition disappears at the hole concentration per Cu of ∼0.28 which coincides with the endpoint of the superconductivity in pristine La_2−xSr_xCuO₄, suggesting that the stripe correlations are closely related to the high-T_c superconductivity in the overdoped regime as well as in the underdoped regime. For the spin-glass state, it has been found that the contribution of polarized itinerant spins to the muon-spin depolarization is not negligible. Taking into account neutron-scattering results obtained by He et al. [Phys. Rev. Lett. 107, 127002 (2011)] that a spin density wave (SDW) order has been observed in overdoped LSCFO, the present results demonstrate the presence of a novel coexistent state of an SDW order of itinerant spins and a spin-glass state of Fe³⁺ spins.