The midfielder joined Tottenham this summer and the Portuguese is backing the Dane to follow in the footsteps of other former Ajax greats
The 21-year-old was one of seven summer signings at White Hart Lane over the summer as Spurs preemptively spent the world-record transfer fee recouped by Gareth Bale's sale to Real Madrid.
|2/1||Christian Eriksen is 2/1 with BetVictor to score anytime against Norwich
"The expectancy is these players will become world stars," Villas-Boas told reporters.
"I think what happened with Christian is a bit like that happened with Sneijder and Van der Vaart when they were at Ajax.
"They reach a moment in their career where they become extremely important for their team and the club who goes and gets them does a great transfer move.
"We expect great things of Christian Eriksen and we want to develop him into becoming that sort of important player for us as well."
Eriksen is expected to make his debut for Tottenham against Norwich City on Saturday, with Villas-Boas stating his selection was a "big possibility".