We study the growth kinetics of nanoclusters in solution. There are two generic factors that drive growth: (a) reactions that produce the nanomaterial; and (b) diffusion of the nanomaterial due to chemical-potential gradients. We model the growth kinetics of ZnO nanoparticles via coupled dynamical equations for the relevant order parameters, We study this model both analytically and numerically. We find that there is a crossover in thenanocluster growth law: from L(t) similar to t(1/2) in the reaction-controlled regime to L(t) t(1/3) in the diffusion-controlled regime.