It is well-known that very preterm children perform at lower levels than full-term children in reading and arithmetic at school. Whether the lower performance levels of preterm children in these two separate domains have the same or different origins, however, is not clear. The present study examined the extent to which prematurity is associated with the overlap (i.e., common variance) of reading and arithmetic among Finnish school beginners. We also examined the extent to which the association of prematurity with the overlap between reading and arithmetic is due to different prereading skills, basic number skills, and general cognitive abilities. The participants (age 6–7) consisted of 193 very preterm children (<32 weeks of gestation or birth weight <1501 g) and 175 full-term control children assessed at the beginning of Grade 1. The results showed that about 40% of the variation in reading and arithmetic skills was common to these two domains and thus, represented the overlap between reading and arithmetic. Prematurity was found to be negatively associated with the overlapping part of reading and arithmetic skills. This association was explained particularly by differences between very preterm and full-term children in prereading (letter knowledge, phonological awareness, and rapid automatized naming) and basic number skills (counting sequence knowledge): Very preterm children showed lower levels of phonological awareness, letter knowledge, counting, and rapid serial naming than full-term children and thus, also demonstrated lower skill level common for reading and arithmetic. Early screening of very preterm children according to the cognitive antecedents that predict the overlap between reading and arithmetic is needed to prevent comorbid difficulties in these domains.