The Vela pulsar is among a number of pulsars which show detectable optical pulsations. We performed optical observations of this pulsar in January and December 2009 with the Iqueye instrument mounted at the ESO 3.5 m New Technology Telescope. Our aim was to perform phase fitting of the Iqueye data, and to measure the optical pulse profile of the Vela pulsar at high time resolution, its absolute phase and rotational period. We calculated for the first time an independent optical timing solution and obtained the most detailed optical pulse profile available to date. Iqueye detected a distinct narrow component on the top of one of the two main optical peaks, which was not resolved in previous observations, and a third statistically significant optical peak not aligned with the radio one. The quality of the Iqueye data allowed us to determine the relative time of arrival of the radio-optical-gamma-ray peaks with an accuracy of a fraction of a millisecond. We compare the shape of the Iqueye pulse profile with that observed in other energy bands and discuss its complex multi-wavelength structure.