We have agreed the transfer of the left-sided player with his club FH Hafnarfjordur and the deal is now subject to personal terms being finalised.
Emil, 20, has played in all of Iceland's European U21 Championship qualifying matches this season as they currently sit second in Group Eight - one of those games a 1-0 defeat to Marton Fulop's Hungary.
Sporting Director Frank said: "First of all, he has been here on trial twice, he had offers from two other clubs but he decided to come to Tottenham.
"He is a left-sided player, a position we have been looking at and he showed so much talent in his time here that we decided to take him.
"It's down the road of bringing in talent, good prospects and giving them a place at Tottenham where they can improve."
Frank Arnesen says he sees Emil Hallfredsson as one for the future after the Icelandic Under-21 international impressed in trials at Spurs Lodge.