The Belgian right-back, 28, is out of contract this summer. He'll sign a four-year deal with the German side that will pay him around €50 million, according to Laurens. Remaining with the Ligue 1 champions was Meunier's preferred option, but he could not agree to terms with the club.
With Achraf Hakimi expected to return to Real Madrid at the end of the season, Dortmund were in the market for a new right-back; the Moroccan's two-year loan spell at the Westfalenstadion is nearing its end.
Dortmund were interested in signing Meunier in 2016, before he left Club Brugge for the French capital, Laurens noted.
Known for his attacking exploits from the right-back position, Meunier has made 16 league appearances for PSG this season, recording two assists.
He's one of four senior PSG players out of contract in the coming months, with left-back Layvin Kurzawa, all-time top scorer Edinson Cavani, and captain Thiago Silva expected to leave the club on free transfers.