  A new class of solutions which yields an $(n+1)$-dimensional spacetime with a
longitudinal nonlinear magnetic field is introduced. These spacetimes have no
curvature singularity and no horizon, and the magnetic field is non singular in
the whole spacetime. They may be interpreted as traversable wormholes which
could be supported by matter not violating the weak energy conditions. We
generalize this class of solutions to the case of rotating solutions and show
that the rotating wormhole solutions have a net electric charge which is
proportional to the magnitude of the rotation parameter, while the static
wormhole has no net electric charge. Finally, we use the counterterm method and
compute the conserved quantities of these spacetimes.
