The distance to the Vela pulsar (PSR B0833-45) has been traditionally assumed to be 500 pc. Although affected by a significant uncertainty, this value stuck to both the pulsar and the supernova remnant. In an effort to obtain a model-free distance measurement, we have applied high-resolution astrometry to the pulsar V ~ 23.6 optical counterpart. Using a set of five Hubble Space Telescope Wide Field Planetary Camera 2 observations, we have obtained the first optical measurement of the annual parallax of the Vela pulsar. The parallax turns out to be 3.4 ± 0.7 mas, implying a distance of 294 pc, i.e., a value significantly lower than previously believed. This affects the estimate of the pulsar absolute luminosity and of its emission efficiency at various wavelengths and confirms the exceptionally high value of Ne toward the Vela pulsar. Finally, the complete parallax database allows for a better measurement of the Vela pulsar proper motion [μα cos(δ) = -37.2 ± 1.2 mas yr-1; μδ = 28.2 ± 1.3 mas yr-1 after correcting for the peculiar motion of the Sun], which, at the parallax distance, implies a transverse velocity of ≈65 km s-1. Moreover, the proper-motion position angle appears especially well aligned with the axis of symmetry of the X-ray nebula as seen by Chandra. Such an alignment allows us to assess the space velocity of the Vela pulsar to be 81 km s-1.