Cell size homeostasis is a basic aspect of coordinated biosynthesis during steady-state growth, yet it was unknown how physiological control and the cell cycle are linked. We show that the cellular resources required to start growth and one round of replication is constant. This "unit cell" size remains invariant under extensive perturbations to replication rate, transcription, translation, ribosome content, lipid and cell wall synthesis, surface-to-volume ratio of the cell, cell shape, and cell division. Instead, the unit cell is exclusively determined by the process of replication initiation. We demonstrate that cell size control in Escherichia coli is completely characterized by three functionally distinct modules - the unit cell, growth and the cell cycle. This leads to the general growth law that cell size is the sum of all unit cells. The general growth law explains how growth and the cell cycle are coordinated and quantitatively predicts cell size for any steady-state growth condition.