We performed muon-spin-rotation/-relaxation measurements to investigate the magnetic behavior of T′-type Eu2CuO4 (ECO), which is the parent compound of electron-doped cuprate superconductors, and the effects of oxygen-reduction annealing on its magnetism. In as-sintered (AS) ECO, we clarified the development of magnetic correlations upon cooling below TN1 (= 265 K) as well as the coexistence of a dominant fluctuating spin state and partially ordered spin state in the temperature range between ∼150 K and TN1. Upon further cooling, uniform long-range magnetic order was observed below TN2=110 K, which is close to the ordering temperature of 115 K in T′-type La2CuO4 (LCO) [Phys. Rev. B 82, 180508(R) (2010)PRBMDO1098-012110.1103/PhysRevB.82.180508]. For oxygen-reduction-annealed ECO, a similar ordering sequence with the same TN2 was observed but without the partially ordered spin state. Therefore, the fluctuating spin state over a wide temperature range and a TN2 less than the Néel temperature (TN2≈TN1) in T-type LCO are common features of the T′-type parent R2CuO4 (RCO, R: rare-earth ion). The origin of the partially ordered spin state in AS ECO is discussed from the viewpoint of chemical defect. Furthermore, we discuss the roles of electron doping and repairing defect in the observed effect of annealing on the magnetism of T′-type RCO.