The Premier League newcomers agreed an undisclosed fee, reported to be £3.5million, with FC Copenhagen for the 27-year-old centre-half, who is a five-time winner of the Danish Superliga and has 11 caps for his country.
He becomes their eighth signing in seven days.
Terriers boss David Wagner said: “Matthias is another very good signing for our club as we prepare for our first Premier League season. 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.”
He began his career at Copenhagen and made nearly 100 appearances before moving to PSV in 2012.
Huddersfield have been busy in the transfer market ahead of their first Premier League season, having already added the likes of Steve Mounie, Laurent Depoitre and Tom Ince in addition to a permanent deal for former loanee Aaron Mooy.