The 29-year-old moved to England from German club Mainz last year on loan and has been an ever-present in the Premier League for the Terriers.
“How he performed on the grass is why we have signed him,” said Wagner. “He has helped us.
“There is still space to improve, but the quality of his distribution has been perfect for the way we play. He has also made big, big saves at important moments. I also think we have seen him improve as the season has gone on.
“This (permanent move) was always something we had in our head. He has helped us to be where we are and he will help us in the future.”
Lossl endured a tough time in the Bundesliga last term and was eventually axed by Mainz. Many observers in Germany were therefore surprised that Wagner was willing to make the Dane his first choice ahead of Town’s Premier League adventure.
The Terriers’ chief said: “It is like always as a manager, you only afterwards know if you made the right decision in signing a player. After Mainz, a lot of people would have said, ‘Don’t do it’.
“There were so many things where we were focused on the positivities. We have done everything right, and Jonas deserves all the credit. He left behind what happened in Mainz and settled in very well with his family.
“He didn’t have the best time last season, but came to the Premier League and performed from day one. He has an opinion that he shows in the dressing room.”
Lossl joins another summer loanee, Swiss international full-back Florent Hadergjonaj, in agreeing a permanent switch to the John Smith’s Stadium in the past week or so.