  We present a Markov Chain Monte Carlo (MCMC)-based parameter estimation
package, CosmoReionMC, to jointly constrain cosmological parameters of the
$\Lambda$CDM model and the astrophysical parameters related to hydrogen
reionization. The package is based on a previously developed physically
motivated semi-analytical model for reionization, a similar semi-analytical
model for computing the global 21~cm signal during the cosmic dawn and using an
appropriately modified version of the publicly available CAMB for computing the
CMB anisotropies. These calculations are then coupled to an MCMC ensemble
sampler \texttt{emcee} to compute the posterior distributions of the model
parameter. The model has twelve free parameters in total: five cosmological and
seven related to the stellar populations. We constrain the parameters by
matching the theoretical predictions with CMB data from Planck, observations
related to the quasar absorption spectra and, for the first time, the global
21~cm signal from EDGES. We find that incorporating the quasar spectra data in
the analysis tightens the bounds on the electron scattering optical depth
$\tau$ and consequently the normalization $A_s$ of the primordial matter power
spectrum (or equivalently $\sigma_8$). Furthermore, when we include the EDGES
data in the analysis, we find that an early population of metal-free stars with
efficient radio emission is necessary to match the absorption amplitude. The
CosmoReionMC package should have interesting future applications, e.g., probing
non-standard extensions to the $\Lambda$CDM model.
