We report the first results of a long term program aiming to provide accurate independent estimates of the Hubble constant (H₀) using the L(Hβ) − σ distance estimator for Giant extragalactic HII regions (GEHR) and HII galaxies. We have used VLT and Subaru high dispersion spectroscopic observations of a local sample of HII galaxies, identified in the SDSS DR7 catalogue in order to re-define and improve the L(Hβ) − σ distance indicator and to determine the Hubble constant. To this end we utilized as local calibration or ‘anchor’ of this correlation, GEHR in nearby galaxies which have accurate distance measurements determined via primary indicators. Using our best sample of 69 nearby Hii galaxies and 23 GEHR in 9 galaxies we obtain H₀ = 74.3± 3.1 (statistical)± 2.9 (systematic) km s⁻¹Mpc⁻¹, in excellent agreement with, and independently confirming, the most recent SNe Ia based results.