In this work, we have investigated the relation between the viscosity and the microscopic dynamics (characterized by the structural relaxation time) of colloidal suspensions, as a function of volume fraction. We have designed and implemented an original setup which allows us to measure the viscoity and the microscopic dynamics simultaneously on the very same sample. The dynamics are measured by conventional multispeckle dynamic light scattering, while the viscosity is obtained by measuring the sedimentation velocity of micron-sized tracer particles. Our measurements extend the range of previous measurements of the zero-shear viscosity about two decades. We find that the viscosity and the relaxation time measured at the peak of the static structure factor are coupled up to deep in the supercooled regime, thereby extending previous observations that were limited to the onset of supercooling. Furthermore, we show that the steep growth of the relaxation time on approaching the glass transition is well described by an exponential divergence, rather than by a critical power law as predicted by Mode Coupling Theory (MCT).