The cultural integration of immigrants conditions their overall socio-economic integration as well as natives’ attitudes towards globalisation in general and immigration in particular. At the same time, excessive integration—or assimilation—can be detrimental in that it implies forfeiting one’s ties to the origin country and eventually translates into a loss of diversity (from the viewpoint of host countries) and of global connections (from the viewpoint of both host and home countries). Cultural integration can be described using two dimensions: the preservation of links to the origin country and culture, which we call origin attachment, and the creation of new links together with the adoption of cultural traits from the new residence country, which we call destination attachment. In this paper we introduce a means to quantify these two aspects based on Twitter data. We build origin and destination attachment indices and analyse their possible determinants (e.g., language proximity, distance between countries), also in relation to Hofstede’s cultural dimension scores. The results stress the importance of language: a common language between origin and destination countries favours origin attachment, as does low proficiency in the host language. Common geographical borders seem to favour both origin and destination attachment. Regarding cultural dimensions, larger differences among origin and destination countries in terms of Individualism, Masculinity and Uncertainty appear to favour destination attachment and lower origin attachment.