The 23-year-old, who joined the principality club from Feyenoord in the summer, will remain in Yorkshire until the end of the season.
Winless in their last four Premier League games, the Terriers were desperate to add more quality to their defensive ranks.
"Terence is a top player who we've followed from his time at Feyenoord," said Wagner. "His big summer move to Monaco put him out of our reach at the time, but we're delighted we can bring him in on loan now.
"He is a high-quality young centre-back and will provide us with a great option for the rest of the Premier League season. With Michael Hefele and Jon Gorenc Stanković returning from long-term injuries, it was important to have this.
"Terence has qualities that will really suit our style of play. He's athletic and mobile and he plays on the front foot in the way he defends and uses the ball. I'm excited to work with him during the course of the season."
DONE DEAL: #htafc has complete the signing of Netherlands international defender @KongoloTerence on loan from @AS_Monacohttps://t.co/qjMA2IGWoU (AT) pic.twitter.com/EhwdEACL4w
— Huddersfield Town (@htafcdotcom) January 2, 2018