Sigurdsson has signed a four-year contract with the Bundesliga club, before immediately departing to join up with the Iceland squad ahead of Euro 2012 qualifiers against Norway and Denmark.
The 20-year-old scored 16 goals in 32 games for Reading, and Hoffenheim are excited to bring him on board.
"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 team manager Ernst Tanner.
Sigurdsson joined Reading as a youngster in 2005, and had loan spells at Crewe and Shrewsbury before breaking into the first team.
Source: PA
