We have prepared the oxyhydride perovskite EuTiO_3-xH_x (x ≤ 0.3) by a low temperature CaH₂ reduction of pyrochlore Eu₂Ti₂O₇ and perovskite EuTiO₃. The reduced EuTiO_3-xH_x crystallizes in the ideal cubic perovskite (Pm3̅m), where O/H anions are randomly distributed. As a result of electron doping by the aliovalent anion exchange, the resistivity of EuTiO_3-xH_x shows metallic temperature dependence. Moreover, an antiferromagnetic-to-ferromagnetic transition is observed even when a small amount of hydride (x ∼ 0.07) is introduced. The Curie temperature T_C of 12 K is higher than those of any other EuTiO₃-derived ferromagnets. The ferromagnetism can be explained by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the Eu(2+) spins mediated by the itinerant Ti 3d electrons. The present study shows that controlling the oxide/hydride ratio is a versatile method to tune magnetic and transport properties.