Coherent control of a system involves steering an interaction to a final coherent state by controlling the phase of an applied field. Plasmas support coherent wave structures that can be generated by intense laser fields. Here, we demonstrate the coherent control of plasma dynamics in a laser wakefield electron acceleration experiment. A genetic algorithm is implemented using a deformable mirror with the electron beam signal as feedback, which allows a heuristic search for the optimal wavefront under laser-plasma conditions that is not known a priori. We are able to improve both the electron beam charge and angular distribution by an order of magnitude. These improvements do not simply correlate with having the 'best' focal spot, as the highest quality vacuum focal spot produces a greatly inferior electron beam, but instead correspond to the particular laser phase front that steers the plasma wave to a final state with optimal accelerating fields.