Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution. © 2017 Informa UK Limited, trading as Taylor & Francis Group.