We report the photoluminescence (PL) and polarization-resolved PL characteristics of a novel GaAs/AlGaAs quantum wire/dot semiconductor system, realized by metalorganic vapor-phase epitaxy of site-controlled, self-assembled nanostructures in inverted tetrahedral pyramids. By systematically changing the length of the quantum wires, we implement a continuous transition between the regimes of two-dimensional and three-dimensional quantum confinement. The two main evidences for this transition are observed experimentally and confirmed theoretically: (i) strongly blue-shifted ground-state emission, accompanied by increase separation of ground and excited transition energies; and (ii) change in the orientation of the main axis of linear polarization of the photoluminescence, from parallel to perpendicular with respect to the wire axis. This latter effect, whose origin is shown to be purely due to quantum confinement and valence band mixing, sets in at wire lengths of only 30 nm.