Reading comprehension skills have been linked to working memory's executive processes such as semantic updating, connecting and integrating information, and inhibition. Different studies have demonstrated that children who score poorly on working memory measures typically perform below expected standards across different academic areas. The aim of this paper is focused on the relationship of executive functions of WM and fluid intelligence with reading comprehension, and their common ability to predict academic achievement in a group of 77 third-grade primary students. As predicted, there was a very clear pattern of positive and significant correlations. Cognitive variables, such as WM's executive processes (particularly semantic updating) and fluid intelligence, correlated with reading variables and two academic measures of language and mathematics. Regression analyses showed that these higher cognitive variables predicted reading comprehension. Likewise, executive processes and reading comprehension, contributed independently to explain a relevant amount of the variance in academic achievement measures.