The inaugural award was presented to the film's producer Klaus Maeck and actress Hanna Schygulla at a plenary session of the parliament in Strasbourg.
The prize will finance the subtitling and video-to-film transfer into the 23 languages of the European Union and an original language adaptation for the deaf and hard of hearing.
Akin's drama was chosen by European Parliament deputies over the other two finalists, Cristian Mungiu's Golden Palm-winner 4 Months, 3 Weeks, And 2 Days and Manoel de Oliveira's Belle Toujours.
The LUX Prize was created by the parliament this year as the European Union celebrated its founding texts and was in the process of drafting a new treaty.
Parliament says the Prize is created 'to illuminate the public debate on European integration and to facilitate the diffusion of European films in the European Union'.
The three finalists were selected by a 17-member jury of industry figures and was screened by MEPs, who could vote for the winner only after seeing all three films.