Experiments on and computer simulations of the migration of fractal, nonwetting fluid bubbles through a two-dimensional random porous medium saturated with wetting fluid are presented. A large invasion percolation bubble was initially formed by slow injection of a nonwetting fluid into a horizontal cell saturated with a denser wetting fluid. Slow, continuous tilting of the cell caused the bubbles to migrate through the medium. The interplay between local pinning forces and buoyancy led to fragmentation and coalescence of migrating bubbles. The process was simulated by a modified site-bond invasion percolation model.