"I'm joining a great club," he told Sky Sports Italia.
"They wanted me here and I'll do my best to repay Inter's faith in me.
"Am I afraid of the competition for a place in the team? No, I'm never scared."The midfielder still has to undergo his medical before joining his new team-mates, as they prepare for their Serie A opener away to Pescara this weekend.
Gargano joins the Nerazzurri on a €1.5 million (£1.2m) loan deal with an option to make his stay permanent next summer for €5m (£3.9m).
While expressing his delight at his move the Uruguay international paid tribute to Napoli and his time at the club.
"The Napoli fans will always remain in my heart,” he continued.
"It was beautiful to play for Napoli, but I'm now starting a new adventure with Inter and I hope to do well.
"Our objective is to always aim for the top because this is a great side."