The 22-year-old will stay on loan with Swansea until the end of the season.
“I’m really pleased that agreement has been reached between the clubs and it is a dream come true for me to get into the Premier League,” said Sigurdsson.
Hoffenheim manager Ernst Tanner said: “Gylfi missed the summer and most of our preparations due to injury.
“We hope that through this loan he will get some much-needed match practice and get back to his former strength.”
