The CGHS two-dimensional dilaton gravity model is generalized to include a ghost Klein-Gordon field, i.e. with negative gravitational coupling. This exotic radiation supports the existence of static traversible wormhole solutions, analogous to Morris-Thorne wormholes. Since the field equations are explicitly integrable, concrete examples can be given of various dynamic wormhole processes. In particular, if the ghost radiation supporting the wormhole is turned off and allowed to disperse, the wormhole collapses into a black hole. The dynamic stability of the wormhole is demonstrated by sending a pulse of radiation through it, forming a non-static wormhole, followed by a pulse of exotic radiation which returns it to a different static state.