Norway midfielder Daehli was taken to Wales by Ole Gunnar Solskjaer, whom he worked with at Molde.
After relegation from the Premier League, Solskjaer departed and since Russell Slade took over at Cardiff in October, Daehli has made just two substitute appearances in the Championship.
On Monday, it was announced that the 19-year-old would join Freiburg - currently bottom of the Bundesliga - in January.
"Mats Moller Daehli is a very interesting player, who we have seen for several years," said Freiburg sporting director Klemens Hartenbach.
"We are therefore very pleased that it worked out and he decided to move to us.
"We gain a technically talented, agile, offensive player who will help our attack in the second half [of the season].
"With his first 19 years he has a considerable experience in the national teams of his country and the English league."
Freiburg also confirmed the acquisition of Petersen, who joins on loan from Bundesliga rivals Bremen.
The 26-year-old forward has made just two league starts for his parent club this season and sporting chief executive Jochen Saier believes it could be a perfect match for both player and club.
"With Nils Petersen we undertook a striker who has already demonstrated his danger in front of goal in recent seasons," he said.
"We are convinced that he will help us with his presence and his final quality. He showed from the first meeting that he's looking for a new start for himself at Freiburg."
