Young moved to San Siro for £1.28 million earlier this month, bringing to an end his eight-and-a-half-year spell at Old Trafford.
Aaron Wan-Bissaka took his spot at right-back for United after joining the club from Crystal Palace.
Young jumped at the chance to link up with Conte at San Siro, two years after rejecting the chance to work under the Italian tactician at Stamford Bridge.
“He wanted me a couple of years ago at Chelsea and he’s a fantastic manager,” Young told Sky Italia.
“He’s won trophies and he’s got an ambition to want to achieve things. I want to do that as well, I want to achieve here at Inter.
“I want to win trophies, I want to win titles and with a manager like that, you want to go out there and fight for him.”
Young went on to explain his decision to leave Old Trafford, citing a lack of regular playing time as the main reason for his departure.
“I had the opportunity to come and play regular football,” he added.
“I wasn’t doing that at Manchester United and I said to the club and the manager that I wanted to go and experience a new chapter in my career. Obviously playing abroad, I’ve never done that.
“To come and play regularly for me was the main thing and that’s what the club had said, that I’d be involved regularly, so I didn’t want to wait until the summer, I wanted to go and play football and that was the opportunity given to me in January.”
Young was handed his full debut for Inter at San Siro last Sunday, laying on an assist during a 1-1 draw against Cagliari, and retained his place in Conte’s starting line up for a 2-1 Coppa Italia quarterfinal win over Fiorentina on Wednesday.