The Morocco international, who started all three of his country's group games at the World Cup in Russia this summer, is being sent to Dortmund to continue his development and will hope for regular first-team football after making 16 senior appearances for Real in all competitions last season.
The 19-year-old is set to join up with his new team-mates on their pre-season tour to the US later this month with the deal announced on the same day Dortmund forward Andriy Yarmolenko exited the club and joined West Ham.
'Achraf Hakimi is a young, very dynamic full-back who has played at the very highest level with Real Madrid and the Morocco national team,' Dortmund sporting director Michael Zorc said.
Celtic skipper Scott Brown insists Champions League football remains key even after more than a decade at the club.
Brighton have completed the signing of midfielder Yves Bissouma on a five-year deal from French side Lille.
Rafael Benitez has admitted he will have to 'wheel and deal' this summer if he is to get the men he wants to rebuild his team.
Joe Hart's future remains up in the air but he has been included in the Manchester City squad for the summer tour to the United States.