Individuals exhibit massive variability in general cognitive skills that affect language processing. This variability is partly developmental. Here, we recruited a large sample of participants (N = 487), ranging from 9 to 90 years of age, and examined the involvement of nonverbal processing speed (assessed using visual and auditory reaction time tasks) and working memory (assessed using forward and backward Digit Span tasks) in a visual world task. Participants saw two objects on the screen and heard a sentence that referred to one of them. In half of the sentences, the target object could be predicted based on verb-selectional restrictions. We observed evidence for anticipatory processing on predictable compared to non-predictable trials. Visual and auditory processing speed had main effects on sentence comprehension and facilitated predictive processing, as evidenced by an interaction. We observed only weak evidence for the involvement of working memory in predictive sentence comprehension. Age had a nonlinear main effect (younger adults responded faster than children and older adults), but it did not differentially modulate predictive and non-predictive processing, nor did it modulate the involvement of processing speed and working memory. Our results contribute to delineating the cognitive skills that are involved in language-vision interactions.