The right-back will officially complete the move to Dortmund when his Paris Saint-Germain contract expires on June 30.
"Borussia Dortmund play exactly the type of football I want to play: exciting, authentic, and natural," Meunier said.
He added: "BVB are known for their enthusiastic fans, and the atmosphere during the match with Paris at the Signal Iduna Park influenced my decision if I'm honest."
Meunier's deal with the German club is worth €50 million, according to Julien Laurens of ESPN.
The 28-year-old is expected to slot right into the starting team next season, as Achraf Hakimi is likely to return to Real Madrid when his loan deal ends.
Meunier made 16 league appearances for PSG before the Ligue 1 season was suspended and eventually canceled due to the coronavirus pandemic.
He won three Ligue 1 titles at PSG after joining them from Club Brugge in 2016.