  An accurate determination of the Hubble constant remains a puzzle in
observational cosmology. The possibility of a new physics has emerged with a
significant tension between the current expansion rate of our Universe measured
from the cosmic microwave background by the Planck satellite and from local
methods. In this paper, new tight estimates on this parameter are obtained by
considering two data sets from galaxy distribution observations: galaxy cluster
gas mass fractions and baryon acoustic oscillation measurements. Priors from
the Big Bang nucleosynthesis (BBN) were also considered. By considering the
flat $\Lambda$CDM and XCDM models, and the non-flat $\Lambda$CDM model, our
main results are: $H_0=65.9^{+1.5}_{-1.5}$ km s$^{-1}$ Mpc$^{-1}$,
$H_0=65.9^{+4.4}_{-4.0}$ km s$^{-1}$ Mpc$^{-1}$ and $H_0=64.3^{+ 4.5}_{- 4.4}$
km s$^{-1}$ Mpc$^{-1}$ in $2\sigma$ c.l., respectively. These estimates are in
full agreement with the Planck satellite results. Our analyses in these
cosmological scenarios also support a negative value for the deceleration
parameter at least in 3$\sigma$ c.l..
