A theory of micellization of AB diblock copolymer molecules in a selective solvent S is developed here. The micelles are assumed to have a completely segregated core region consisting only of the A block and a shell region consisting of the solvent S and the solvent compatible B block. The theory allows one to predict the critical micelle concentration, the micelle size distribution, the average aggregation number, as well as the core radius and the shell thickness of the micelle. The novel outcome of the present theory, in contrast to the treatments of micellization pioneered by de Gennes, Leibler, Orland, and Wheeler, and Noolandi and Hong, is its prediction that the solvent compatible B block plays an important role in determining the micellization behavior. The influence of the B block becomes relatively more prominent in systems where the solvent S constitutes a very good solvent for the B block. Further, scaling relations that are not system specific have been developed relating explicitly the micellar size parameters to the characteristics of the block copolymer and the solvent.