The Portuguese boss made the pair his first acquisitions following his appointment on a three-year deal at White Hart Lane and has praised their respective qualities
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.
"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."