The Portugal international, who is currently representing his country at Euro 2016, leaves Les Merlus after three seasons, where he was almost ever-present in the first team.
Guerreiro is comfortable in either defence or attack and will provide competition for Marcel Schmelzer and Erik Durm in Thomas Tuchel's team after penning a long-term contract until 2020.
"Raphael Guerreiro is a technically-skilled player who feels at home in several positions," BVB sporting director Michael Zorc told the club's official website. "We are very happy that he has chosen Borussia Dortmund."
The 22-year-old came through the youth ranks at Caen and spent one season as a first-team regular before he made the switch to Brittany in 2013.
Guerreiro joins a host of new signings at Dortmund, including Ousmane Dembele from Rennes, Nordsjælland's Emre Mor and Mikel Merino from Osasuna.