We report measurements of the fluorescence lifetimes of positronium (Ps) atoms with principal quantum numbers n=10–19. Ps atoms in Rydberg-Stark states were produced via a two-color two-step 1S3→2P3→nS3/nD3 excitation scheme and subsequently detected after traveling 1.2 m. The measured time-of-flight distributions were used to determine the mean lifetimes of the Rydberg levels, yielding values ranging from 3μs to 26μs. Our data are in accord with the expected radiative lifetimes of Rydberg-Stark states of Ps
