  We investigate the formation of a new type of composite topological
excitation -- the skyrmion-vortex pair (SVP) -- in hybrid systems consisting of
coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the
superconductor mediates a magnetoelectric coupling between the vortex and the
skyrmion, with a sign (attractive or repulsive) that depends on the topological
indices of the constituents. We determine the conditions under which a bound
SVP is formed, and characterize the range and depth of the effective binding
potential through analytical estimates and numerical simulations. Furthermore,
we develop a semiclassical description of the coupled skyrmion-vortex dynamics
and discuss how SVPs can be controlled by applied spin currents.
