  The strategy of obtaining the familiar Kerr-Newman solution in general
relativity is based on either using the metric ansatz in the Kerr-Schild form,
or applying the method of complex coordinate transformation to a non-rotating
charged black hole. In practice, this amounts to an appropriate re-scaling of
the mass parameter in the metric of uncharged black holes. Using a similar
approach, we assume a special metric ansatz in N+1 dimensions and present a new
analytic solution to the Einstein-Maxwell system of equations. It describes
rotating charged black holes with a single angular momentum in the limit of
slow rotation. We also give the metric for a slowly rotating charged black hole
with two independent angular momenta in five dimensions. We compute the
gyromagnetic ratio of these black holes which corresponds to the value g=N-1.
