Cosmic reionization and dark matter decay can impact observations of the cosmic microwave sky in a similar way. A simultaneous study of both effects is required to constrain unstable dark matter from cosmic microwave background observations. We compare two reionization models with and without dark matter decay. We use the Planck 2015 data to constrain the effective decay rate of dark matter to $\Gamma_{\rm eff} <  2.9 \times 10^{-25}/$s at $95$\% C.L. This limit is robust and model independent. It holds for any type of decaying dark matter and it depends only weakly on the chosen parametrization of astrophysical reionization. For light dark matter particles that decay exclusively into electromagnetic components this implies a limit of $\Gamma <  5.3 \times 10^{-26}/$s at $95$\% C.L. Specifying the decay channels, we apply our result to the case of keV-mass sterile neutrinos as dark matter candidates and obtain constraints on their mixing angle and mass, which are comparable to the ones from the diffuse X-ray background.