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 $2sigma$ 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..
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