Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha }$ is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins $N$. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a $d$-dimensional system including the absence of localization in the infinite system at $\alpha <2d$ and a universal scaling of a critical energy disordering $W_c\propto N^{\frac{2d-\alpha }{d}}$.

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