Belgium international Vertonghen, 25, has completed his move from Ajax following a medical, to join Iceland midfielder Sigurdsson, who enjoyed a successful loan spell at Swansea last season, at White Hart Lane.
"They give us further solutions," Villas-Boas said. "Sigurdsson had a tremendous impact in the Premier League last season. With the interest around him, for him to join Tottenham with this ambition is something we are grateful for."
He added: "Jan is tremendously experienced and can play in a number of positions, which is another thing we look for in the way we build our squad."
Former Chelsea manager Villas-Boas was appointed successor to Harry Redknapp as Spurs looked to take a new direction.
The Portuguese coach believes his squad is shaping up nicely ahead of the new campaign. Former Spurs midfielder Steffen Freund has been installed as assistant head coach, while some of the old backroom staff in Tim Sherwood and Les Ferdinand have been retained.
Villas-Boas said: "We have put together the right technical staff and mixture of competence.
"We have mixed in Tottenham's tradition, and are also bridging the gap with the development squad, which is important."
Spurs led the challenge to Manchester City and Manchester United for much of last season, only to then fade badly over the closing months. Villas-Boas, however, sees no reason why the squad should not kick on again.
"When you join a club of this dimension, you are given the possibilities for success, and there are more probabilities for that to happen," said the Portuguese coach, who penned a three-year deal at White Hart Lane less than six months after being axed by Chelsea.
Source: PA
Source: PA