Cortical resting state networks have been consistently identified in infants using resting state-functional connectivity magnetic resonance imaging (rs-fMRI). Comparable studies in adults have demonstrated cerebellar components of well-established cerebral networks. However, there has been limited investigation of early cerebellar functional connectivity. We acquired non-sedated rs-fMRI data in the first week of life in 57 healthy, term-born infants and at term-equivalent postmenstrual age in 20 very preterm infants (mean birth gestational age 27 ± 2 weeks) without significant cerebral or cerebellar injury. Seed correlation analyses were performed using regions of interests spanning the cortical and subcortical gray matter and cerebellum. Parallel analyses were performed using rs-fMRI data acquired in 100 healthy adults. Our results demonstrate that cortico-cerebellar functional connectivity is well-established by term. Intra- and cortico-cerebellar functional connectivity were largely similar in infants and adults. However, infants showed more functional connectivity structure within the cerebellum, including stronger homotopic correlations and more robust anterior-posterior anticorrelations. Prematurity was associated with reduced correlation magnitudes, but no alterations in intra- and cortico-cerebellar functional connectivity topography. These results add to the growing evidence that the cerebellum plays an important role in shaping early brain development during infancy.