Writing is a complex academic task—it involves numerous mental processes. Given the necessity for developing writing skills from elementary to secondary school, this study aimed to investigate the role of broad cognitive abilities derived from the Cattell–Horn–Carroll (CHC) theory of intelligence in predicting skills associated with writing achievement. The normative sample from the fourth edition of the Woodcock–Johnson Tests of Cognitive Abilities and the Woodcock–Johnson Tests Academic Achievement were used to examine the relationships between broad CHC abilities and academic achievement in writing. The findings of this study suggest that the broad CHC abilities Comprehension‐Knowledge, Processing Speed, and Fluid Reasoning are especially important predictors of basic writing skills and written expression during the school‐age years. In general, changes in the strength of the association between cognitive abilities and academic achievement in writing are observed over time, as the cognitive demands involved in the writing increase in complexity in later grades.