The Iceland international becomes Andre Villas-Boas’ first signing since being named as Tottenham manager.
Spurs managed to beat Liverpool and Swansea in the race to sign the 22-year-old midfielder.
A statement on Tottenham’s website read: “We are delighted to announce that we have completed the transfer of Gylfi Sigurdsson from Hoffenheim.
“The attacking midfielder is no stranger to the Premier League having enjoyed an impressive loan spell at Swansea City during the second half of last season.
“He scored seven times in 19 appearances as well as picking up the Barclay’s Player of the Month award for March.
“The Iceland international originally moved to England with Reading, coming through their academy to make 51 appearances and scoring 23 times. He was named Player of the Year in his only full season in the Royals First Team before moving to the Bundesliga with Hoffenheim in 2010.”
Sigurdsson impressed while on loan at Swansea last season.
