The Iceland international previously played for Reading and left the club last year after Hoffenheim came in with an offer in excess of the Royals' transfer record of £6.5million.
The 22-year-old attacking midfielder has since played 36 league games for Hoffenheim, scoring nine times.
The German side's manager Ernst Tanner told his club's official website: "Gylfi missed the summer and most of our preparations due to injury and did not really kick on after that.
"We now hope that through this loan he will get some much needed match practice and get back to his former strength."
Sigurdsson welcomed the chance to play in the Premier League, as well as the opportunity to reprise his relationship with boss Brendan Rodgers.
"I'm really pleased that agreement has been reached between the clubs and it is a dream is true for me to get into the Premier League," said Sigurdsson in quotes carried by Swansea's official website.
"I follow the Premier League very closely and I have both seen and heard Swansea play good football.
"It does not surprise me because I played under manager Brendan Rodgers at Reading and he wants his team to play the ball from the last man."