The cosmic distance scale largely depends on distance determinations to Local Group galaxies. In this sense, the Andromeda Galaxy (M31) is a key rung to better constrain the cosmic distance ladder. A project was started in 1999 to firmly establish a direct and accurate distance to M31 using eclipsing binaries (EBs). After the determination of the first direct distance to M31 from EBs, the second direct distance to an EB system is presented: M31V_J00443610+4129194. Light and radial velocity curves were obtained and fitted to derive the masses and radii of the components. The acquired spectra were combined and disentangled to determine the temperature of the components. The analysis of the studied EB resulted in a distance determination to M31 of (m-M)o = 24.30 +/- 0.11 mag. This result, when combined with the previous distance determination to M31, results in a distance modulus of (m-M)o = 24.36 +/- 0.08 mag (744 +/- 33 kpc), fully compatible with other distance determinations to M31. With an error of only 4%, the obtained value firmly establishes the distance to this important galaxy and represents the fulfillment of the main goal of our project. ; Comment: 7 pages, 3 figures, accepted for publication in A&A (Nov 6, 2009)