Short-term memory (STM) is required for second language learning. However, it is not clear what components of STM are necessary for the acquisition and lexicalisation of new written words. Studies suggest that memory for serial order is a critical cognitive process in spoken word acquisition although correlated mechanisms such as executive control also play a role. In this study, bilingual Cantonese–English speakers who are learning written expert words in a non-native language were tested over a one year period in their first year of instruction. Written word lexicalisation was measured using lexical decision and spelling to dictation tasks. Results showed measures of executive control (Stroop performance) and serial order memory capacity predict recognition and recall of written expert words at different stages. Whereas serial order memory predicts improvements to lexical decision accuracy, executive control predicts spelling to dictation performance after one year. The conclusion is that STM processes do constrain written word lexicalisation in a second language. However, executive control and serial order memory capacity have differential effects during word lexicalisation.