We demonstrate a method to grow height controlled, dislocation-free InGaAs quantum posts (QPs) on GaAs by molecular beam epitaxy (MBE) which is confirmed by structural investigations. The optical properties are compared to realistic 8-band k.p calculations of the electronic structure which fully account for strain and the structural properties of the QP. Using QPs embedded in n-i-p junctions we find wide range tunability of the interband spectrum and giant static dipole moments.