Because of lacking intrinsic magnetism, developing efficient methods for the magnetism engineering in two-dimensional (2D) materials is necessary in order to make new spintronic materials. In this work, doping and codoping with transition metals (TMs = Mn and Fe) is proposed to modify the arsenene monolayer electronic and magnetic properties. Bare monolayer is intrinsically nonmagnetic, exhibiting semiconductor character with an indirect gap of 1.60 eV. Mn and Fe substitution induces significant magnetism, giving place to overall magnetic moments of 4.00 and 5.00 mB, respectively, being produced primarily by TM impurities. Moreover, Mn impurity induces the half-metallicity with perfect spin polarization at the Fermi level, while the magnetic semiconductor nature is obtained by Fe substitution. In both cases, perpendicular magnetic anisotropy (PMA) is confirmed through calculating magnetic anisotropy energy. In addition, the ferromagnetic (FM) phase is energetically stable, exhibiting smaller energy than antiferromagnetic (AFM) and ferrimagnetic (FiM) phases. Robust ferromagnetism is achieved by small TM–TM interatomic distance with high Curie temperature up to 1192.19 K. Further separating transition metal impurities will weaken the ferromagnetism, decreasing significantly Curie temperature. Moreover, it is demonstrated also that Mn–Mn separation switches the electronic nature from magnetic semiconductor to half-metallic, meanwhile the half-metallicity is obtained in the cases of Fe doping and Mn/Fe codoping regardless TM–TM separation. Controlling TM–TM separation is also predicted to effectively regulate the system magnetic anisotropy, inducing the PMA-to-IMA (in-plane magnetic anisotropy) switching and vice verse. Our findings may introduce efficient doping approaches to get ferromagnetism in arsenene monolayer, which can form promising 2D candidates for selective spintronic applications.