Flower production and crop yields are highly influenced by the architectures of inflorescences. In the compound inflorescences of tomato and related nightshades (Solanaceae), new lateral inflorescence branches develop on the flanks of older branches that have terminated in flowers through a program of plant growth known as "sympodial." Variability in the number and organization of sympodial branches produces a remarkable array of inflorescence architectures, but little is known about the mechanisms underlying sympodial growth and branching diversity. One hypothesis is that the rate of termination modulates branching. By performing deep sequencing of transcriptomes, we have captured gene expression dynamics from individual shoot meristems in tomato as they gradually transition from a vegetative state to a terminal flower. Surprisingly, we find thousands of age-dependent expression changes, even when there is little change in meristem morphology. From these data, we reveal that meristem maturation is an extremely gradual process defined molecularly by a "meristem maturation clock." Using hundreds of stage-enriched marker genes that compose this clock, we show that extreme branching, conditioned by loss of expression of the COMPOUND INFLORESCENCE gene, is driven by delaying the maturation of both apical and lateral meristems. In contrast, we find that wild tomato species display a delayed maturation only in apical meristems, which leads to modest branching. Our systems genetics approach reveals that the program for inflorescence branching is initiated surprisingly early during meristem maturation and that evolutionary diversity in inflorescence architecture is modulated by heterochronic shifts in the acquisition of floral fate.