An exact magnetohydrodynamic solution is presented for steady magnetic annihilation (merging) in an incompressible resistive viscous plasma. The merging, driven by an axisymmetric stagnation flow on a cylinder, takes place in a curved current sheet that is perpendicular to the plane in which the plasma flow stagnates. The new solution extends earlier models of flux pileup merging in a flat current sheet, driven by stagnation-point flows. The new solution remains valid in the presence of both the isotropic and anisotropic (parallel) plasma viscosity. The geometry of the solution may make it useful in modeling the photospheric flux cancellation on the Sun.