The Dresselhaus spin-orbit interaction (SOI) of a series of two-dimensional electron gases (2DEGs) hosted in GaAs/AlGaAs and InGaAs/GaAs (001) quantum wells (QWs) is measured by monitoring the precession frequency of the spins as a function of an in-plane electric field. The measured spin-orbit-induced spin-splitting is linear in the drift velocity, even in the regime where the cubic Dresselhaus SOI is important. We relate the measured splitting to the Dresselhaus coupling parameter, the QW confinement, the Fermi wavenumber and to strain effects. From this, the coupling parameter is determined quantitatively, including its sign.