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We have investigated the magnetic properties of ${\mathrm{EuTi}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}{\mathrm{O}}_{3}$ with $0\ensuremath{\le}x\ensuremath{\le}1$ and established a detailed magnetic phase diagram. Substitution of ${\mathrm{Ti}}^{4+}$ with ${\mathrm{Al}}^{3+}$, which oxidizes magnetic ${\mathrm{Eu}}^{2+}$ $(J=7/2)$ into nonmagnetic ${\mathrm{Eu}}^{3+}$ $(J=0)$, turns the antiferromagnetic insulating ground state $(x=0)$ into the ferromagnetic (FM) insulating one $(0.10\ensuremath{\le}x\ensuremath{\le}0.50)$. The ${\mathrm{Eu}}^{2+}/{\mathrm{Eu}}^{3+}$ mixed valence is indispensable for the FM behavior. In $0.10\ensuremath{\le}x\ensuremath{\le}0.33$, the Curie temperature ${T}_{\mathrm{C}}$ has a plateau at $\ensuremath{\sim}4$ K, and the FM correlation is most enhanced around $x=0.25$. In $0.33\ensuremath{\le}x\ensuremath{\le}1,{\mathrm{Al}}^{3+}$ substitution suppresses the FM correlation due to the dilution of magnetic ${\mathrm{Eu}}^{2+}$ ions. Our present results would provide useful information for magnetoelectric phase control of ${\mathrm{EuTiO}}_{3}$-based compounds.