Spurs signed the midfielder from West Ham for a reported fee of 85 million pounds after moving quickly to secure his signature before Manchester United could make their own bid.
Fernandes is expected to resume full training when Tottenham return to London next week after missing Friday's open training session at Accor Stadium because of a minor knock.
The Portugal international endured relegation with West Ham last season, but Tottenham identified him as one of De Zerbi's priority signings as the Italian looks to build a younger, technically gifted midfield.
Fernandes said De Zerbi's conversations with both him and his family convinced him that Tottenham was the right club.
"The way he spoke with me and my family was very important for me," Fernandes told *The Athletic*.
"He was calling me every day, so I'm very happy to work with him, and hopefully we can do great things."
Fernandes explained that the discussions went beyond football because his parents are not fluent in English.
"It was more about forming a connection, because my dad and my mum don't speak English very well. It was more about feelings."
"He said he would take care of me, that he would be my second dad in England. I'm very happy to work with him."
Tottenham defender Pedro Porro also helped persuade Fernandes to join the club.
According to Fernandes, Porro urged him to make the move, telling him: "Come on Mateus, you need to play with us, we want you."
Fernandes added that Porro also joked: "It was me that told the manager to bring you."
The midfielder is expected to form a new-look partnership with Sandro Tonali in Tottenham's midfield as De Zerbi continues reshaping his squad ahead of the new season.
Chelsea play Juventus next in a pre-season friendly match on Wednesday at the Kai Tak Stadium in Hong Kong.
