This paper investigates to what extent the wealth accumulation of immigrants is explained by their degree of assimilation, defined as the immigrants' capacity to become more similar over time to the local people in terms of their norms, values, behaviours, and socioeconomic characteristics. The existing practice to measure assimilation is the use of a time-dimensioned variable like years since migration, which reflects the individual's adaptation to the host country through the implied acquisition of relevant skills and experience. We complement this approach by defining assimilation on the basis of migrants' subjective assessments of integration within the community. To do so, we exploit the rich information collected by the Household Income and Labour Dynamics in Australia Survey (HILDA). In particular, we explore the possible relationship between migrants' savings and assimilation estimating several models, from a pooled OLS to panel data models such as random effect and population average. We find that assimilation has a significant positive effect on wealth accumulation, but in different degrees depending on migrants origins and the type of assets. Understanding migrants' wealth and their perceived degree of assimilation is relevant to understand the supply of domestic savings and their variability. It also carries policy implications on what could be done to affect migrants' sense of assimilation and connected economic behaviour.