The paper presents a theoretical study of the effect of different atomic and magnetic orderings on the structural and magnetic properties of Mn2Ni1+xTi1-x alloys, which are composed entirely of transition metals. Using the density functional theory, we predict the structural ground states and magnetic reference states of compounds with x = 0, 0,25, 0,5, and 0,75 in both cubic austenite and tetragonal martensite phases. Partial substitution of Ti atoms with Ni leads to an increase in the energy barrier between structural phases, to a change from a layered atomic ordering to an alternating staggered order, and to a change from antiferromagnetic to ferromagnetic spin alignment in the cubic phase. All compounds with tetragonally distorted structures reveal the out-ofplane spin configuration and easy axis magnetocrystalline anisotropy except tetragonal L10 phase of Mn2NiTi. For the latter structure, easy-plane magnetic anisotropy is observed. The calculated values of anisotropy are comparable with those of tetragonal L10-FeNi.