Русско-англо-русский юридический словарь

Family reunification is a recognized reason for immigration in many countries because of the presence of one or more family members in a certain country, therefore, enables the rest of the divided family or only specific members of the family to emigrate to that country as well. (Wikipedia)

Family Reunification vs Family Reunion. Both terms are used interchangeably by international bodies (Council of Europe, European Union, Unesco etc.) and no specific scope has been identified for either. The Parliamentary Assembly of the Council of Europe (PACE), for example, uses ‘family reunion’ [e.g. in Recommendation 1686 (2004)] but more often “family reunification��� [e.g. in Rec 1703 (2005)]. (Council of Europe)

Convention refugees can travel to 20 European Union countries visa-free and have an explicit right to family reunification under section 56 of the International Protection Act 2015. (Dublin Inquirer)