The magnetic properties of Fe_{1 - x} Co _x B and (Fe_{1 - x} Co _x )₂B disordered compounds were investigated using first-principles calculations of the electronic structure in the framework of the density functional theory with the Korringa-Kohn-Rostoker method. The concentration dependences of the magnetic moments and the electron density were calculated for the Fe_{1 - x} Co _x B solid solutions. The results obtained were used to analyze in detail and to interpret the transition from a magnetic phase to a nonmagnetic phase, which was previously revealed from the experiments in the compounds under investigation. The performed analysis of the calculated hyperfine fields induced by the electronic shells at the iron and cobalt atoms in the (Fe_{1 - x} Co _x )₂B borides made it possible to explain the experimentally observed magnetic anisotropy.