40 pages, 23 figures (including 4 available as separate figures), to be published in Astroparticle Physics ; The ANTARES neutrino telescope is a large photomultiplier array designed to detect neutrino-induced upward-going muons by their Cherenkov radiation. Understanding the absorption and scattering of light in the deep Mediterranean is fundamental to optimising the design and performance of the detector. This paper presents measurements of blue and UV light transmission at the ANTARES site taken between 1997 and 2000. The derived values for the scattering length and the angular distribution of particulate scattering were found to be highly correlated, and results are therefore presented in terms of an absorption length lambda_abs and an effective scattering length lambda_sct^eff. The values for blue (UV) light are found to be lambda_abs ~ 60(26) m, lambda_sct^eff ~ 265(122) m, with significant (15%) time variability. Finally, the results of ANTARES simulations showing the effect of these water properties on the anticipated performance of the detector are presented.