An integrated Kinetic Monte Carlo structure-rheology model is developed for polyolefins produced using solution copolymerization of ethylene and alpha-olefins. The proposed algorithm is completely first-principle and can be used to simulate any homogeneous single-site polymerization process resulting in full topological and chemical composition details of the product formed. The model maintains simple hierarchical data structures to track the structure and composition of polymer chains and efficiently generates a full ensemble of polymeric molecules under varying process conditions. The model has a control-volume description with no implicit assumptions regarding the dynamic state of the process, and hence the methodology can be used for any reactor configuration. We benchmark the model by simulating two semibatch pilot plant runs and use the benchmarked model to simulate production of three industrial grade polyolefins which differ significantly in their molecular weight distributions, long-chain branching fractions, and chemical composition. For modeling the continuous state production process with the control volume description, we propose a simple inflow/outflow step in the algorithm to model continuous stirred-tank reactors (CSTR) which eliminates use of idealized flow and steady-state approximations. The simulated molecular topology and bivariate long-chain branching (LCB) molecular weight distributions are used to select a representative ensemble of molecules that is used to calculate linear rheology using the branch-on-branch model of Das et al. The resulting product distributions for the semibatch trials reproduce the measured molecular weight distributions. For the polyolefins simulated with the continuous process the virtual products have closely matching molecular weight distributions and branching fractions compared to measured values of the industrial polyolefins. The simulated rheology also agrees quite closely with the experimental values without use of any fitting parameters in the full integrated approach. In addition, microstructural characteristics as measured by the crystallization elution fractionation technique also match closely with the simulated crystallization elution fractionation distributions calculated using the longest ethylene sequence distributions obtained for the three products.