The 49-year-old was named as Luciano Spalletti's successor on May 31 to end his year-long exile from the game since being dismissed by Chelsea.
Conte returns to the Italian top flight five years after leaving Juventus, where he won five major honours, including three successive Serie A crowns.
Juve are considered Inter's fiercest rivals, but the ex-Italy boss insists coaching multiple clubs "is normal" and says he is ready to end his new club's trophy drought, which spans eight years since they lifted the Coppa Italia.
Conte, who also spent 13 years with the Turin giants during his playing days, told GQ Italia: "It’s normal to work for different clubs. I look forward to bringing Inter where they belong. The fans expect a lot, and they do well to support the team.
"I must work very hard. I need to work, it's in my DNA. I can accept having only a little chance of winning at first, but that must change. We can win things, we have no limits."
Conte had also been tipped to replace Massimiliano Allegri at former club Juventus, but he was persuaded to begin a new adventure with Inter after holding talks with chief executive Giuseppe Marotta and chairman Steven Zhang.
"The presence of Marotta helped me join Inter because it was confirmation that they had very serious intentions," he said.
"For eight seasons, they haven't fought for first place. They want to change that, and I was struck by Zhang's determination.
"I know there are expectations placed on me, given the results I've achieved and the speed with which they came."
Inter finished the 2018-19 campaign fourth in Serie A, 21 points adrift of champions Juventus.