The early years of life are important for immune development and influence health in adulthood. Although it has been established that the gut bacterial microbiome is rapidly acquired after birth, less is known about the viral microbiome (or 'virome'), consisting of bacteriophages and eukaryotic RNA and DNA viruses, during the first years of life. Here, we characterized the gut virome and bacterial microbiome in a longitudinal cohort of healthy infant twins. The virome and bacterial microbiome were more similar between co-twins than between unrelated infants. From birth to 2 years of age, the eukaryotic virome and the bacterial microbiome expanded, but this was accompanied by a contraction of and shift in the bacteriophage virome composition. The bacteriophage-bacteria relationship begins from birth with a high predator-low prey dynamic, consistent with the Lotka-Volterra prey model. Thus, in contrast to the stable microbiome observed in adults, the infant microbiome is highly dynamic and associated with early life changes in the composition of bacteria, viruses and bacteriophages with age.