We investigated the role of linguistic and cognitive processes in reading precocity from kindergarten to grade 2. A sample of 33 precocious readers was identified that did not differ on age, gender, and parental education to a control group of 259 typical readers. The effects of verbal ability were also controlled. All children were administered a battery of cognitive and linguistic measures in three assessment points at the midterm of each year. Individual growth modeling (IGM) was used to test the rate and shape of change of the two groups. Results showed that precocious readers exhibited superior performance in phonological awareness, naming speed, and reading fluency, across development, whereas their early advantage in letter knowledge disappeared by grade 1. A cognitive advantage specific to executive function (planning) was also observed for the precocious readers early on and was maintained through grade 2. Precocious readers outperformed the control group also on silent word reading, reading comprehension, and on the expressive (production) and the receptive (recognition) orthographic processing tasks. We concluded that both linguistic and cognitive abilities—independent of verbal ability—underlie individual differences in reading precocity.