Phosphorus is one of the potential light elements of the core of the Earth and other planets. The high-pressure behavior of phosphorus compounds with nickel and iron attracts considerable attention due to their abundance in iron meteorites. In the present work, with modern methods of crystal structure prediction, we investigate the structures and stability of compounds in the Ni-P system at pressures of 100-400 GPa. As a result, a homologous series of discrete compounds (Ni, P), consisting of Ni14P, Ni12P, Ni10 P, Ni8P, Ni7P, Ni5P, and Ni3P was found. Phosphorus shows sufficient solubility in the face-centered cubic (fcc) structure of Ni, and up to 25 mol % of this element can be dissolved at low temperatures. Based on the comparison of compounds in the Ni-P and Fe-P systems, we suggest that at high pressures Ni facilitates phosphorus dissolution in the closed-packed structure of d-metals, and dissolution of P in the (Ni, P) alloy will be higher than that in pure Fe. For the Ni3P compound, a new high-pressure phase with the Cmca symmetry is predicted. This structure can be described as deformed fcc packing and also belongs to the ordered representatives of the series of (Ni, P) solid solutions. The transition from the low-pressure phase of Ni3P-I4¯ to the Cmca phase occurs at a pressure of 62 GPa, regardless of the external temperature. Ni2P is stabilized at a pressure above 200 GPa in the form of an allabogdanite structure. The transition from transjordanite to allabogdanite occurs at 78-88 GPa and 0-2000 K.