The magnetic order of the localized Eu$^{2+}$ spins in optimally-doped Eu(Fe$_{1-x}$Ir$_{x}$)$_{2}$As$_{2}$ ($mathit{x}$ = 0.12) with superconducting transition temperature $mathit{T_{SC}}$ = 22 K was investigated by single-crystal neutron diffraction. The Eu$^{2+}$ moments were found to be ferromagnetically aligned along the $mathit{c}$-direction with an ordered moment of 7.0(1) $mu_{B}$ well below the magnetic phase transition temperature $mathit{T_{C}}$ = 17 K. No evidence of the tetragonal-to-orthorhombic structural phase transition was found in this compound within the experimental uncertainty, in which the spin-density-wave (SDW) order of the Fe sublattice is supposed to be completely suppressed and the superconductivity gets fully developed. The ferromagnetic groud state of the Eu$^{2+}$ spins in Eu(Fe$_{0.88}$Ir$_{0.12}$)$_{2}$As$_{2}$ was supported by the first-principles density functional calculation. In addition, comparison of the electronic structure calculations between Eu(Fe$_{0.875}$Ir$_{0.125}$)$_{2}$As$_{2}$ and the parent compound EuFe$_{2}$As$_{2}$ indicates stronger hybridization and more expanded bandwith due to the Ir substitution, which together with the introduction of electrons might work against the Fe-SDW in favor of the superconductivity.
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