The study explores whether foundational skills of reading and spelling in preschool (age 5–6) predict literacy skills cross-linguistically in an additional language in Grade 1 (age 6–7). A sample of linguistically diverse preschool children completed tasks of phonological awareness, letter-sound knowledge, verbal-short term memory, rapid automatized naming, and lexical knowledge in the language of preschool instruction Luxembourgish. The children were followed-up in Grade 1 where literacy skills were assessed in the language of schooling, i.e., German, after five months of literacy instruction. German was a non-native language for all children. Longitudinal correlations confirm that individual differences in single word/pseudoword reading and spelling in German in Grade 1 can be predicted by all the foundational literacy skills that were assessed in Luxembourgish. Path analyses showed that phonological awareness in Luxembourgish emerged as the strongest unique predictor of Grade 1 literacy skills in German. The second unique preschool predictor of Grade 1 literacy skills was letter-sound knowledge. Results are consistent with the view that literacy development in an additional language builds upon similar building blocks as literacy acquisition in a first language, at least for languages that are typologically close. However, current findings suggest that respective contributions between predictors and literacy skills in children learning to read in an additional language may vary from patterns observed in studies with children acquiring literacy in their first language.