The Icelandic midfielder secured his move from Hoffenheim, after turning down the opportunity to link up again with Brendan Rodgers at Liverpool.
Meanwhile, Vertonghen's long-running transfer saga came to an end on Thursday, as he completed a move from Dutch champions Ajax, and his new manager had nothing but praise for the defender.
"Jan has not [been] through the Premier League experience but he is a player that has a very, very solid career at Ajax and became Ajax captain.
"He is a player who leads by example, is very determined and with a great personality and also is one of the players who fits what we want to achieve in terms of style of play - which is part of Tottenham’s tradition and part of the culture that I defend.
"He’s a central defender who likes to come out with the ball to organise the team. He is quick and aggressive so I think he has the right ingredients to become a top player in the Premier League."
The former Porto boss also had kind words for Sigurdsson, who enjoyed a successful loan spell with Swansea toward the end of last season.
"Gylfi is of course player who exploded last season with Swansea in the last six months," Villas-Boas added.
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"A player that had previously been in England so knew the environment, was given an opportunity with Swansea and impressed everybody.
"He was a target for most of the top clubs this season and it’s important for us to get a player that makes excellent movements.
"He has a great scoring ability and also organises the team in difficult positions and then finds the decisive pass.
"[The pair are] excellent signings to improve the squad so that we can push forward for what we want."