Sigurdsson considered joining the Reds because of the presence of his former Swansea City boss Brendan Rodgers.
"I enjoyed playing under Brendan and I am grateful for everything he has done for me, but after careful consideration I liked Spurs best," Sigurdsson told mbl.is.
"The team has world-class players in their ranks and they play good football, which I like. I was impressed with the club's plans for next season and the coming years.
"There is clearly great ambition at Tottenham and the club intends to do big things. It is a pleasure to see that Gareth Bale has signed a new contract.
"There are top players in the team and the club is getting a new training ground."