The signing of the 27-year-old Danish striker Jorgensen makes it 10 new signings for manager David Wagner after he scooped up Scott Malone, record-signing Steve Mounie, Tom Ince, Danny Williams, Kasey Palmer on loan, Elias Kachunga, Laurent Depoitre, Aaron Mooy and Jonas Lossl.
Jorgensen has penned a three-year contract with the newly-promoted side
Wagner told the club's official website: "Mathias is another very good signing for our club.
"He is a very complete defender with great experience of being successful in every league he has played in, which served us well with the signings we made last season too.
"His athleticism and football intelligence will be big assets in the Premier League, for sure, and he is a super professional character, which will fit in with our current group of players very well.
"This deal makes total sense for us because Jon Stankovic is out of action until Christmas."
"Zanka" as he is known, began his career with Copenhagen before joining PSV. He returned to the Danish side in 2014, and has gone on to win the Danish Superliga five times and the Danish Cup five times.
Midfielder Dean Whitehead has, meanwhile, signed a one-year contract extension and defender Fraser Horsfall has joined Gateshead on a loan deal for the first half of next season.
Wagner added: "After the Play-Off Final I had an honest and open conversation with Dean about the Premier League and his role in our team.
“We shared our thoughts on what we both expect from the upcoming season and agreed that even if he plays less for us, he is still a very important part of the team and our dressing room.
“I am very happy that he will be at this club for a further season; he is a true professional and a really good character.”
And finally, Paul Clements has been confirmed as the club's new Head of Goalkeeping, stepping up from his previous role as Lead Academy Goalkeeping Coach. He replaces Nick Colgan.