Iceland Under-21 international Emil arrives from Icelandic champions FH Hafnarfjordur on a two-and-a-half year deal.
Meanwhile, Czech Under-21 international David (pictured left) joins us on a six-month loan arrangement with an option to make the switch permanent.
Emil, 20, has played in all of Iceland's European U21 Championship qualifying matches this season.
Sporting director Frank Arnesen sadi: "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."
Emil added: "It's excellent, a dream come true for me to come to a team like Tottenham. Many boys have this dream in Iceland but few get a chance like this."
David, 22 on Thursday, joins from Czech Division Two side Viktoria Plzen
Frank said: "David is quick footed, has good awareness, is an intelligent footballer and can play on either side of midfield.
"These players are down the road of bringing in talent, good prospects and giving them a place at Tottenham where they can improve."
We have completed the deals to bring Emil Hallfredsson and David Limbersky to the club - their registrations will be finalised once we receive international clearance from their respective countries.