Magnetic double perovskite (DP) compounds provide a fertile playground to explore interesting electronic and magnetic properties. By complementary macroscopic characterizations, neutron powder diffraction measurements, and first-principles calculations, we have performed comprehensive studies on the magnetic ordering in the DP compound Sr2NiWO6. It is found by neutron diffraction to order magnetically in a collinear type-II antiferromagnetic (AFM) structure in a tetragonal lattice with k=(0.5,0,0.5) below TN=56K. In the ground state, the ordered moment of the spin-1 Ni2+ ions is determined to be 1.9(2)µB, indicating a significant quenching of the orbital moment. The Ni2+ moments in Sr2NiWO6 are revealed to cant off the c axis by 29.2∘, which is well supported by the first-principles magnetic anisotropy energy calculations. Furthermore, the in-plane and out-of-plane next-nearest-neighbor superexchange couplings (J2 and J2c) are found to play a dominant role in the spin Hamiltonian of Sr2NiWO6, which accounts for the stabilization of the type-II AFM structure as its magnetic ground state.