Different language skills are considered fundamental for successful reading and spelling acquisition. Extensive evidence has highlighted the central role of phonological awareness in early literacy experiences. However, many orthographic systems also require the contribution of morphological awareness. The goal of this study was to examine the morphological and phonological awareness skills of preschool children as longitudinal predictors of reading and spelling ability by the end of first grade, controlling for the effects of receptive and expressive vocabulary skills. At Time 1 preschool children from kindergartens in the Greek regions of Attika, Crete, Macedonia, and Thessaly were assessed on tasks tapping receptive and expressive vocabulary, phonological awareness (syllable and phoneme), and morphological awareness (inflectional and derivational). Tasks were administered through an Android application for mobile devices (tablets) featuring automatic application of ceiling rules. At Time 2 one year later the same children attending first grade were assessed on measures of word and pseudoword reading, text reading fluency, text reading comprehension, and spelling. Complete data from 104 children are available. Hierarchical linear regression and commonality analyses were conducted for each outcome variable. Reading accuracy for both words and pseudowords was predicted not only by phonological awareness, as expected, but also by morphological awareness, suggesting that understanding the functional role of word parts supports the developing phonology–orthography mappings. However, only phonological awareness predicted text reading fluency at this age. Longitudinal prediction of reading comprehension by both receptive vocabulary and morphological awareness was already evident at this age, as expected. Finally, spelling was predicted by preschool phonological awareness, as expected, as well as by morphological awareness, the contribution of which is expected to increase due to the spelling demands of Greek inflectional and derivational suffixes introduced at later grades.