The characteristics of electronic states of Cd-vacancies in CdTe, an important semiconductor for various technological applications, are under debate both from theoretical and experimental points of view. Experimentally, the Cd-vacancy in its negative charge state is found to have C3v symmetry and a (-1/-2) transition level at 0.4 eV. Our first principles density functional calculations with hybrid functionals confirm for the first time these experimental findings. Additionally, we find that the C3v symmetry and the position of the (-1/-2) transition level are caused by the formation of a hole polaron localised at an anionic site around the vacancy.