The striker arrives from Hoffenheim where he played for the past six years after coming through the Energie Cottbus youth system.
"I'm really excited to take this next major step in my career," said Beier, who scored 16 goals in 33 games in his first full Bundesliga season.
He also received his first senior international call-up in March and was part of Julian Nagelsmann's Germany squad for the European Championship.
Dortmund sporting director Sebastian Kehl said Beier was the club's "top target" after Niclas Fullkrug's departure for English Premier League club West Ham.
"He's very self-assured on the pitch despite his young age, and he has impressive pace, he never stops running and he poses a real goal threat," said Kehl.
"On top of that, he has the versatility to play in several positions and in various systems. There's scope for him to develop further, and we'll help him become an even better player.
"He's a down-to-earth person who's willing to learn, and his hard work and commitment make him the perfect fit for BVB."
