Adjoint based shape optimization methods have proven to be computationally efficient for aerodynamic problems. The majority of the studies on adjoint methods have used structured grids to discretize the computational domain. Due to the potential advantages of unstructured grids for complex configurations, in this study we have developed and validated a continuous adjoint formulation for unstructured grids. The hurdles posed in the computation of the gradient for unstructured grids are resolved by using a reduced gradient formulation. Methods to impose thickness constraints on unstructured grids are also discussed. Results for two and three dimensional simulations of airfoils and wings in transonic flow are used to validate the design procedure. Finally, the design procedure is applied to redesign the shape of a transonic business jet configuration, and we were able to reduce the drag of the aircraft from 235 to 216 counts resulting in a shock free wing.