The Belgian pair, who play alongside the winger internationally, told the former Twente man he "had to come" to Spurs, who the 24-year-old believes were his best option this summer
The former Twente winger joined the club in July and could make his first appearance for the club in a preseason friendly against Monaco on Saturday after training with the squad on its recent tour of Hong Kong.
Chadli has made 14 appearances for Belgium and says compatriots Vertonghen and Dembele played a crucial role in convincing him to move to White Hart Lane.
"They said a lot of good things about Spurs," Chadli told the club's official website. "They said ‘you have to come’. I was very happy I made the transfer. I’ve already played with them for the national team and we have good contact.
"I expect a lot from myself this year and I hope I can make everyone happy."
Chadli scored twice for former club Twente against Tottenham, as they met in the 2010-11 Champions League.
The 24-year-old was impressed with the experience of playing the London club, and believes it also helped make his mind up about where he would play this season.
"I remember playing at White Hart Lane, we lost 4-1 but I scored the goal for Twente," he said. "I came on after 15 minutes because of an injury and it was unbelievable, the stadium, the feel of the pitch, the supporters [were] so for the team and I liked it.
"Some clubs wanted me this summer but Tottenham Hotspur was the best choice for me and the best club, a club I can fit in to. I played here three years ago for Twente and I was really impressed with the club, the stadium and all the players."