Regulatory problems in infancy and toddlerhood have previously been associated with an increased risk of developing attention problems in childhood. We hypothesized that early regulatory problems are associated with attention problems via reduced inhibitory control. This prospective study assessed 1,459 children from birth to 8 years. Crying, feeding, and sleeping problems were assessed at 5 and 20 months via parent interviews and neurological examinations. At 20 months, inhibitory control was tested with a behavioral (snack delay) task. Attention regulation was assessed at 6 and 8 years using multiple instruments and informants. Detrimental effects of crying, feeding, and sleeping problems on attention regulation were partly mediated by children's ability to inhibit unwanted behaviors (β = −0.04, p = 0.013). Accounting for cognition diminished this indirect effect (β = −0.01, p = 0.209). Instead, the effects of crying, feeding, and sleeping problems on attention regulation were fully mediated by children's cognitive functioning (β = −0.10, p < 0.001). These results support that inhibitory control abilities partly mediate effects of crying, feeding, and sleeping problems. However, these effects may be accounted for by children's general cognitive abilities. Early regulatory problems may set infants on a course of under control of behavior into school age, and such trajectories are highly associated with general cognitive development.