Okay, I've gathered the answers from the comments in alphabetical order.

1. flint has the fmpz_poly_revert_series command (A web search revealed a reference pdf, but no web page). Some benchmarks seem to indicate that flint is unusually fast.

2. Maple has the reversion command.

3. Mathematica has the InverseSeries command.

4. Pari/GP has the serreverse function.

5. SAGE has the reversion command.