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;,ab, and an effective scattering length lambda(sct)(eff). The values for blue (UV) light are found to be lambda(abs) similar or equal to 60(26) m, lambda(sct)(eff similar or equal to) 265(122) m, with significant (similar to15%) time variability. Finally, the results of ANTARES simulations showing the effect of these water properties on the anticipated performance of the detector are presented.