Sigurdsson, 22, who previously played for Swansea manager Brendan Rogers at Reading, has joined on loan until the end of the season, Swansea and Hoffenheim said on their official websites.
Swansea climbed to 11th in the standings after winning 2-0 at Aston Villa on Monday and Sigurdsson joins Rory Donnelly, a promising 19-year-old striker from Northern Ireland side Cliftonville, as a new arrival at the Liberty Stadium.
Hoffenheim manager Ernst Tanner told his club's official website: "Gylfi missed a large part of pre-season with an injury and it was hard for him coming back into the first team when he did.
"We hope that he can accumulate the necessary match practice during this loan spell and find the form he showed when he first arrived here."
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