We report a theoretical and experimental study of the aggregation kinetics of oppositely charged nanoparticles. Kinetic Monte Carlo simulations are performed for symmetric, charge-asymmetric and size-asymmetric systems of oppositely charged nanoparticles. Simulation results show that both the weight and number average aggregate size kinetics exhibit power law scaling with different exponents for small and intermediate time of evolution. The qualitative behavior of the symmetric and the size asymmetric system are the same, but the charge asymmetric system shows anomalous behavior for intermediate to high particle concentrations. We also observe a strong dependence of power law exponents on the particle concentration. Radius of gyration of the cluster that indicates how nanoparticles inside a cluster are distributed around the center of mass of the cluster shows a non-monotonic time evolution with pronounced peak at higher particle concentration. The dependence of particle concentration on aggregation kinetics as observed by predictive numerical simulation is further verified experimentally by monitoring the time evolution of aggregate size of nanoparticles assemblies of Poly (methacrylic acid) (PMMA) nanoparticles functionalized with oppositely charged ligands. These size and charge tunable asymmetric polymeric nanoparticles were synthesized by modified miniemulsion technique. The integrated approach for studying nanoparticles aggregation as described here renders new insights into super structure formation and morphology optimization which can be potentially useful in the design of new materials, such as organic photovoltaics.