Spin dephasing via the spin-orbit interaction (SOI) is a major mechanism limiting the electron spin lifetime in III-V zincblende quantum wells (QWs). The dephasing can be suppressed in GaAs(111) quantum wells by applying an electric field. The suppression has been attributed to the compensation of the intrinsic SOI associated with the bulk inversion asymmetry of the GaAs lattice by a structural induced asymmetry SOI term induced by an electric field. We provide direct experimental evidence for this mechanism by demonstrating the transition between the bulk inversion asymmetry-dominated to a structural induced asymmetry-dominated regime via photoluminescence measurements carried out over a wide range of applied fields. Spin lifetimes exceeding 100 ns are obtained near the compensating electric field, thus making GaAs(111) QWs excellent candidates for the electrical storage and manipulation of spins.