We consider the ejection dynamics of a flexible polymer chain out of confined environment. This situation arises in different physical contexts, including a flexible synthetic polymer partially confined in a nanopore and a viral genome partially ejected from its capsid. We describe the chain release from confinement both analytically and by means of dynamic Monte Carlo simulation. We find two distinct regimes of ejection dynamics depending on whether the chain is fully or partially confined. Partially confined chains are ejected from a pore of length L and diameter D after a typical time tau proportional to (LD5/3)-D-2, regardless of their contour length N. The process is driven by a constant force f approximate to 5k(B)T/D and follows a "capillary" law. The force value is model-independent as long as the pore diameter exceeds the persistence length of the polymer chain and for pore walls that do not attract the segments of the polymer. In contrast, the ejection of fully confined chains is largely diffusive, the residence time being a nonmonotonic function of N. The drift-dominated ejection of long chains is characterized by narrow distribution of exit times whereas for diffusive-dominated ejection the exit times are described by a broad distribution. One finds good agreement with recent nanofluidic experiments with DNA.