The 20-year-old joins the Bundesliga outfit in a deal worth around £6million, according to reports.
The Iceland international has signed a four-year contract with Hoffenheim.
“Gylfi Sigurdsson, although only 20 years old, has a great ability to score from midfield and we still see in him huge potential to develop further,” said Hoffenheim team manager Ernst Tanner.
Sigurdsson scored 16 goals in 32 games during his time at Reading.
