This is one of the profiles in the Administrator (AD) open competitions, though in some cases Assistant (AST) or contract agent (CAST) exams may have translation-related profiles announced as well. Translators are usually required to have a diploma but there is no obligation to have one in translation or language studies so as to ensure that candidates with a broad range of profiles are eligible. Translators are employed by all EU institutions, and many work in Luxembourg for the European Parliament or the Council of Ministers in Brussels.
See also:
Linguist | Interpreter | Administrator | Assistant | CAST | EU Institutions | European Parliament | Council of Ministers
Related link:
Language Rules | Selection and Recruitment | Reserve List