Variation in the branching of plant inflorescences determines flower number and, consequently, reproductive success and crop yield. Nightshade (Solanaceae) species are models for a widespread, yet poorly understood, program of eudicot growth, where short side branches are initiated upon floral termination. This "sympodial" program produces the few-flowered tomato inflorescence, but the classical mutants compound inflorescence (s) and anantha (an) are highly branched, and s bears hundreds of flowers. Here we show that S and AN, which encode a homeobox transcription factor and an F-box protein, respectively, control inflorescence architecture by promoting successive stages in the progression of an inflorescence meristem to floral specification. S and AN are sequentially expressed during this gradual phase transition, and the loss of either gene delays flower formation, resulting in additional branching. Independently arisen alleles of s account for inflorescence variation among domesticated tomatoes, and an stimulates branching in pepper plants that normally have solitary flowers. Our results suggest that variation of Solanaceae inflorescences is modulated through temporal changes in the acquisition of floral fate, providing a flexible evolutionary mechanism to elaborate sympodial inflorescence shoots.