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It is shown that extremal magnetic black hole solutions of N=2 supergr avity coupled to vector multiplets X(Lambda) with a generic holomorphi c prepotential F(X(Lambda)) can be described as supersymmetric soliton s which interpolate between maximally symmetric limiting solutions at spatial infinity and the horizon. A simple exact solution is found for the special case that the ratios of the X(Lambda) are real, and it is seen that the logarithm of the conformal factor of the spatial metric equals the Kahler potential on the vector multiplet moduli space. Sev eral examples are discussed in detail.