The Belgium international put pen to paper on a four-year deal at the Westfalenstadion.
Dortmund beat Tottenham Hotspur to Meunier's signature as they hope to build a team which can finally break Bayern Munich's stranglehold on Bundesliga, with the Bavarians winning the last eight league titles.
"Thomas Meunier is a player who has proven his quality at the highest level, among other things in the Champions League and in the national team, over a long period of time and will give us a real boost with his experience," Zorc said of the third Belgium international in the current squad - midfielder Axel Witsel and winger Thorgan Hazard being the two others.
Meunier began his career at Club Brugge and spent the last four seasons at PSG for whom he made a total of 17 Champions League appearances over the years and he said that, among other things, he was attracted by the club's raucous fans he experienced during February's Champions League to Dortmund with PSG.
"Borussia Dortmund play exactly the type of football I want to play: exciting, authentic and natural," he said. "BVB are known for their enthusiastic fans, and the atmosphere at the Westfalenstadion that day influenced my decision if I'm honest. I am ambitious and I want to win titles with Dortmund, as I have done in Brugge and Paris."
Speaking at a news conference earlier on Thursday, Dortmund sporting director Zorc said that the club will not give up on Achraf Hakimi, who is set to return to Real Madrid following a two-year loan spell at Borussia.
"We are interested in finding a solution with Real and Achraf so he might play football at Dortmund again next season," he reiterated the club's stance over the past few weeks.