  We give an 11 and 10 dimensional supergravity description of M5-branes
wrapping 4-cylces in a Calabi-Yau manifold and carrying momentum along a
transverse S$^1$. These wrapped branes descend to a class of N=2 black holes in
4 dimensions. Our description gives the conditions on the geometry
interpolating between the asymptotic and near-horizon regions. We employ the
ideas of geometric transitions to show that the near horizon geometry in ten
dimensions is AdS$_2\times$S$^2\times CY_3$ while in 11 dimensions it is
AdS$_3\times$S$^2\times CY_3$. We also show how to obtain the complete N=2
black hole supergravity solution in 4 dimensions for this class of black holes
starting with our 11-dimensional description. Finally, we generalize our
results on the 10 and 11 dimensional near horizon supergravity solution to the
case of black holes carrying arbitrary charges (D0-D2-D4-D6 in the type IIA
description). We argue that the near horizon geometry corresponding to wrapped
D6 and D2 branes in 11 dimensions is AdS$_2\times$S$^3\times CY_3$.
