Proxima and Alpha Centauri AB have almost identical distances and proper motions with respect to the Sun. Although the probability of such similar parameters is in principle very low, the question as to whether they actually form a single gravitationally bound triple system has been open since the discovery of Proxima one century ago. Owing to HARPS high precision absolute radial velocity measurements and the recent revision of the parameters of the Alpha Cen pair, we show that Proxima and alpha Cen are gravitationally bound with a high degree of confidence. The orbital period of Proxima is approximately approximate to 550 000 years. With an excentricity of 0.50(-0.09)(+0.08), Proxima comes within 4.3(-0.9)(+1.1)) kau of alpha Cen at periastron. Its orbital phase is currently close to apastron (13.0(-0.1)(+0.3) kau). This orbital motion may have influenced the formation or evolution of the recently discovered planet orbiting Proxima as well as circumbinary planet formation around alpha Cen.