We perform an analysis of the cosmic reionization in the standard cold dark matter (CDM) paradigm and in alternative dark matter scenarios. Building upon the work of Corasaniti et al., we predict the reionization history for CDM, for warm dark matter, late-forming dark matter and ultralight axion dark matter models which reproduce state-of-the-art measurements of the galaxy luminosity function at very high redshifts 6≤z≤10. To this purpose we adopt a reionization model parametrized in terms of the limiting UV magnitude of galaxies contributing to the reionization Mlim and the average effective escape fraction of UV photons reaching the intergalactic medium f˜. For each DM model we compute the redshift evolution of the Thomson scattering optical depth τe(z) and the comoving ionization fraction QHII(z). We find the different DM models to have similar reionization histories. Differences with respect to the CDM case increase at fainter limiting UV magnitudes and are degenerate with the effect of varying the reionization model parameters. Using Planck’s determination of the integrated optical depth in combination with measurements of the neutral hydrogen fraction at different redshifts, we infer constraints on f˜ and Mlim. The results are largely independent of the assumed DM scenario; in particular for Mlim≳-13 we obtain that the effective escape fraction lies in the range 0.07≲f˜≲0.15 at 2σ.